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Equation of a plane

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Hello again, everyone. This is Tom from everystepcalculus.com, everystepphysics.com. A problem with the equation of a plane that I found on Yahoo questions from a student. And I’m going to answer it in my programs here. Index 8 to my menu scroll down here to equation of a plane now and your calculator you can go second and which is quicker with your fingers and go screen by screen down to in the menu. There’s equation of a tangent plane is not what we’re looking for a look at our equation of a plane right there. There it is. And we’re given a point and a line in the problem. You have to press alpha before you enter anything into these entry lines, here. The point is 1 alpha 6 and alpha minus 4. These again all contrived problems, they never happen in real life ever. It’s just crunching numbers for no reason which is perfect for calculus. Calculus is like studying crossword puzzles to learn English. It’s a waste of time, in my opinion. But we have to pass your test we have to get through this course which you’re required to take so that’s the reason I program it for myself and I’m program for you. There’s the poin.t I say it’s ok I give you a chance to change in cases not. We’re gonna add a parametric line equation which is alpha 1+2 times t.
and the y value is alpha 2-3 times t. and the z value is alpha 3 – t. Again I show you what you’ve entered you can change. it looks pretty good to me. It’s a vector now. That’s what these little indications here are. It’s called a vector. I say it’s ok. So we do the calculations. We take T equal to zero, we come up with 1, 2, 3, here. At t equals 1 you put that in the problem. substitute one in for t’s. you’ll put parentheses in here, I have to put quotation marks because the calculation can’t go to let me do anything different and so then therefore we have 3-1 2. We have our 3 points for a plane ab&c. Here they are. And now we’re going to go find a vector from point c to b which is called vector d. I call it vector d, I call it vector d is equal to 1, 2, 3 minus the 3 minus 1 2. We do those calculations and we come up with this. Vector c to a, vector e is this. 1 6 minus 4, 3 minus 1, 2. We’re going to find the normal perpendicular well normal is perpendicular to the two vectors. Cross product, they call it normal but I mean I like to do it practical. And we’re gonna cross product d times e the two we just found which is these times this ok. Now, you try to do this from memory. Go ahead, try it; not me. It’s a waste of time. So anyway, here’s the the actual calculations. Matrix calculation multiplication and we’re doing these calculations. Make sure you write these on
your paper, now. and equals minus 25 14 8. That’s the normal vector to the two vectors we found. And so we do computations of the equation of a plane, etc Make sure you write all this in your paper, exactly like to see. And the answer is minus 25 X plus minus 14 y plus minus eight z plus 77 equals 0. pretty neat, huh? everystepcalculus.com. Go to my site, buy my programs, pass calculus. You’ll burn your calculus book but you’ll never throw away the calculator with my programs ever because you never know when your life who your partner is or your grandkids or somebody’s gonna do calculus eventually and you have all this in your calculator from then on. Have a good one.

Vector Function on TI-89 & Titanium

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Hello everyone, Tom from everystepcalculus.com everystepphysics.com, a quick example of
vector valued function, r(t) formula, or vector function. And with regard to speed. So, let’s do it. Index 8 to get to my menu. We’re gonna scroll up to get to the bottom of the menu so that we’re closer to the s section; it’s all alphabetical. I choose speed. Speed is a scaler, meaning it has no direction, it has magnitude, but no direction. Unless time is added to it, and then it does have a direction. You’re gonna enter these values here, but if Z is not given you’re gonna enter 0, okay? So, you have to press alpha before you enter anything in these entry lines here. Alpha minus 3 times T Alpha 2 times T Alpha minus 6 times T. I always show you what you’ve entered, you can change it if you want. There’s the vector. These indicate that it’s a vector, these arrows here. Say it’s okay. Now we’re gonna choose speed, we’re looking for speed. It’s right there. And it’s given by the magnitude. Magnitude is the derivative of the function times the squares of each one of them. So it’s X prime of t squared, y prime of t squared, z prime of t squared. And the derivatives are minus 3, 2, and minus 6. And we square them. Asks if there’s time given, I’d say there’s no time given in this one. So we’re gonna choose number 2. And then just square the values, sum them up,
49, and there’s the answer: 7 units per second. Pretty neat, huh? everystepcalculus.com, go to my site, buy my programs, and subscribe if you want to see other videos. Have a good one.

Vectors-Magnitude of A times B

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Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. This is an everystepcalculus.com problem. And with my programs. Question on vectors. Let’s get started. Index 8 to get to my menu. Choose A and B vectors. This is a Calculus 3 problem. This student wanted to know how to find the magnitude of A times B. He could get the cross product but he do the magnitude of it. So, let me know you how to do that. You have to enter Alpha before you enter anything into these entry lines, here. So, Alpha minus 2. Alpha one. Alpha one. For the B Vector. Alpha 2, Alpha 1. Alpha 1. So we check see if that’s the vectors that you want. I say it’s okay. A times B is the cross product so we’re going to go to here, A times B. Matrix Multiplication. Write this on your paper, exactly as you see it. There’s the Cartesian System. Notating a vector. Right here. And here’s the answer for the cross product. Zero, four, four. So, we have one vector now which is 0 for X, 4 for Y, and minus four for Z. So now we’re going to go down and we’re gonna find new AB vectors. As we need to put a new vector in for A. So the answer was Alpha zero, Alpha four. That’s for the cross product. Alpha minus four. And we can just quickly go through these because there is no vector for B of A. So now we’re going to go up here and find magnitude of, magnitude of A, number 2. Choose that. This is the way you notate it, it’s got these two lines on the side. It’s called the magnitude of A. Do these calculations. Notice the square root of x square, y squared, z squared and we come up with 5.66 units. Pretty neat, huh? everystepcalculus.com. Have a good one.

Cross Product A & B Test Question Example-Video

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Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. Cross Product with regards to A and B Vectors. It’s a Calculus 3 Vector problem. Let’s do it. Index 8 to get to my menu. We’re going to scroll to Cross Product. Add the vectors. Alpha 8. You have to add Alpha before you enter anything into my menus. Alpha 9, Alpha minus 4. That’s vector A. Vector B is Alpha minus 7, Alpha 8, Alpha minus 3. I always show you what you’ve entered. You can change it if you want. I say it’s okay. We’re going to scroll down to Cross Product. There’s Cross Product. A times B cross product and B times A cross product. Whichever one, they’re different. We’re going to do A times B. And it’s a matrix situation, that’s for sure. So you write these down. Make sure that you keep these in the rows that you have. Make sure you write exactly what you see, here. All these equations. This is I J, and K. That’s a different vector format. 5, 52j, 127k. and here’s the vector situation with the arrows here. 5, 52, 127. Pretty neat, huh? That’s a tough problem if you don’t have a programs, if you don’t know what you’re doing. Especially on a test or something. Go to my site, subscribe so you can see more videos. Have a good one.

Cosine A & B Test Question Example-Video

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Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. I’m going to do a problem for Cosine of A & B which is a Calculus 3 problem in Vectors. Let’s do it. Index 8 to get to my menu. There’s cosine of A and B, here. I’m going to add the vectors. Press Alpha first. Alpha 7, enter. Alpha minus 9, enter. Alpha minus 8, enter. Second vector B. Alpha minus 12, Alpha 8, Alpha minus 6. I always show you entered so you can change it if you made a mistake. I say it’s okay. And we’re going to scroll down here to the C’s. And there’s cosine of A and B. Here’s the formula. Dot product of A and B divided by the magnitude of A and the magnitude of B. So here’s the system that you write on your paper. Multiply this times this. And then we’re doing the magnitudes of A which is the square root of all these squares here and same thing with B. You want to try this without the program, go right ahead. It turns to be minus 108 over the square root of 194 times the square root of 244. Square root of 47 thousand. Cosine of minus 1 arc cosine of this here equals approximately 120 degrees, 2.09 radians. Go to my sites, subscribe so you can see more videos, if you want. Have a good one.Have a good one.

A & B Vector Solutions

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Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. A and B vectors. This is Calculus 3, usually. Let’s get started. Index 8 to get to my menu. You’re going to have A anB vectors choose number two here. We’re gonna add the vectors. You have to press Alpha before you enter anything into my entry lines. Alpha 9. That’s the X value. If we have all the X and Y than just put zero in for Z. Alpha minus five alpha 7. That’s the first vector. Now we’re going to do the B vector for XYZ. Alpha 15 Alpha minus 4 Alpha 6. I always show you what you’ve entered. These arrows here are vectors; notations. I say it’s okay. Now you have all these choices. For instances, you want to subtract them, you choose number 4. Try this without this program if you want to try it. You’re going to mess up a minus sign. That’s what I always did or something. Got something wrong . number seven magnitude. The magnitude is this vector plus this vector. You have to that and then you have to take, then you have to multiply or use the under the square root sign. Square root of x squared y squared Z squared. Turns out to be twenty eight point seven four units. If you do number 8 . That’s for three vectors. I’ll ask you to enter the C vector. Scroll down here to cosine of A and B. That’s always fun to do. In other words, the angle between the vectors. That turns out to be this formula here. A times B times the magnitude. Add all this exactly on your paper. It’s just the way you do that computations yourself. Turns out to be 18.1 degrees and point 315 radians. Pretty neat, huh? everystepcalculus.com Go to site, subscribe for more videos. Thank you.

Vector Cross Product on TI-89-Video

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This is a calculus calculator program or App for vector cross product using the TI-89 calculator to get to my main menu you press second alpha to enter the letters i_n_d_e_x and then press alpha again to enter the 8 and open and close parentheses press enter and you into my menu you have many choices in this menu difference quotient dot product eliminating the parameter equation of a line all kinds of choices for calculus one two and three here’s e to the ex derivative we’re gonna demonstrate the cross product here so we’re gonna scroll up to cross product press enter and were going to enter our two vectors you have to press alpha before you enter any variables in this calculus calculator program enter 8 alpha :00 alpha minus 9 here is the B vector alpha five alpha seven alpha 3. I’ll show you what you’ve entered you can change it if you want and we have another menu comes up which is all you can do with these vectors B minus A A times dot product or A times B dot product equation of a plane component of A direction of U. I’m gonna do you can do AB cross product or BA cross product lets do AB and here’s the vectors that your multiplying time its a matrix multiplication when you write everything down in your paper in this calculus calculator program just as you see it on the screen here to get an A on this problem pretty neat huh, EveryStepCalculus.com goto my site enjoy my programs and pass calculus.

Vector Dot Product

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This is a ti-89 program app demonstrating my programs and how they do
vector dot product uh… we’re going to get started here, you have to press second alpha to enter the letters i n d e x and then press alpha again to enter the eight and open and closed parenthesis. Press enter and you’re into my menu. you have many options here for passing tests and homework in my menu here many things integration by parts integration by parts inflection points and graphing by hand uh… e to the x integrals we’re going to scroll up to dot product gonna enter our first vector _a you have to press alpha before you enter anything in my entry lines alpha eight alpha minus three alpha minus five _b vector alpha seven
alpha nine, alpha two. I show you what you’ve entered case you made a mistake you can change it. I say it’s okay. this is the menu for all of my vectors. uh… many things here projection of a and b all kinds of things that you’re going to be calculus two probably and we’re going to scroll down to _v section here and find dot product. Write everything down on your paper exactly as you see it and gives you the total answer here. Pretty neat huh? everystepcalculus.com enjoy my programs and pass calculus.

Pre Calculus Help | Vectors | Cross Product | TI89 Software App

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Pre Calculus Help Video: Vectors

How the TI89 solves preCalc A & B Vectors:

  • Bring up the menu and scroll to A & B Vectors
  • Enter the vectors or the variables of the two vectors
  • The program shows you what’s entered and asks if you would like to change it
  • Scroll and choose what you would like to solve: A,B Magnitude, A-B Magnitude, A+B Magnitude, A+B+C, Cross Product, B-A, A * B dot product, Area of Parallelogram
  • View answer with all work shown

Raw Transcript

Hey this is tom the calculus and physics guy who programs the TI89 calculators and other calculators for the TI system. uh…today or this video I’m going to be talking about or showing you how fabulous my programs work on vectors my site is EveryStepCalculus.com and enjoy my program.

This is two vectors in space uh… starting from the origin to x_y_z_ uh… points you notice we start again from the index8() and in the home screen to get to my programs and up comes a menu with all these different types of things that you can compute and we want to do the vectors today so we’re gonna do a-b and vectors.

We add the first one is it asking for thex_y_z_ point of the first vector  uh… vector a again and x_y_z_ and alpha 8 alpha minus seven, alpha minus three, vector b alpha six, alpha minus five, alpha seven shows us what we have if that’s correct and you can go here and press ok.

Now you notice they have the magnitude of vector a choose that one and you can see where the magnitude comes to eleven units uh… shows you how to do it eight squared you know square root of 8 squared minus seven squared minus three squared.

Go back vector B same thing press the this shows you how to do that part uh… a minus b all these different vector calculations come up I wanted to do them when I was in college quickly and not waste time with it and get them exactly accurate.

Vector a minus b is 2 minus b minus 10 if you want to find the magnitude of a minus b you can go a minus b and find that the shows you how to do exactly that putting in the variables dot product and then we’ll move on here got all these different choices.

A cross product…length B times a cross product B times A there’s a difference uh… constants against a times b times a area of a parallelogram component of A in direction of B equation of a plane all these things cross product is pretty cool ’cause that’s a matrix system and shows you there and then does all the calculations for you and there’s the in the cartesian system i j k system or the vector system with the arrows on the ends of it. Pretty neat huh? Enjoy my programs at EveryStepCalculus.com.

Vector Dot Product | Calculus App | TI89 | EveryStepCalculus

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This is a pre calculus help video on vector dot product, actually a program app for the ti 89 titanium calculator. To get to my main menu. You press 2nd alpha to enter the letters I n d e x and then press alpha to enter the eight and the closed parenthesis you Press ENTER and you’re into my main menu. You scroll to where your choice is, right now you want to know how to do vector dot product so we’re going to scroll to dot product in my menu. Press ENTER now we need to add the vectors or the variables of the two vectors and so follow along as I do that you have to press alpha first alpha eight for the x alpha minus three alpha minus nine alpha seven alpha five alpha minus two. I show you what you’ve entered you can change it if you want I say it’s ok. And you can do many things with these two vectors but today we want to do vector dot product so Im going to scroll up to A B times dot product heres the way you notate the vector with a dot in between to show that your doing a dot product heres your vectors 8 times 7 minus 3 times 5 minus 9 times minus 2 and that calculates to 56 plus minus 15 plus 189 which is 59, pretty neat huh everyStepCalculus.com. Got to my site, enjoy my programs, and pass calculus.

 

Calculus -Vectors – Program App – TI-89 Titanium Calculator

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This is a video on vectors, and let’s get started here. You have to press second alpha to get to the letters of my menu code, i n d e x and then press alpha again and put in the eight and the closed parenthesis, and press enter and you are into my program, you’ll notice you can scroll down to get to the a b c’s of the beginning of it a and b vectors but you know that’s also goes to vectors but we can go, scroll down in case you want to call it just plain vectors, and we’re going to press enter and get into the vectors program. Press alpha before you put anything in here, were going to press alpha eight, alpha minus twelve, alpha nine, for vector b, the x y z coordinates, we’re going to put in alpha seven, alpha minus thirteen, and alpha minus fifteen, I tell you what you’ve entered so you can change it if you want, I say it’s ok, I’m going to press number one and we’re into all the different functions, if you want to find the magnitude of vector B, press three, and do the calculations, shows you what your doing here and you get absolutely do all the calculations, square root et cetera. We can go a plus b, number 6, a plus b, eight twelve, et cetera, come up with the a plus b answer. We can have a plus b plus c it’ll, three vectors find their resultant and components. We have to enter the vector c, alpha eight, alpha six, alpha minus two and again check whether we’re doing it, vectors a b and c , resultant, b minus a et cetera, let’s do the cosine, cosine between a and b, that’s the formula there, you write all this stuff on your paper of course, and we’re doing the dot product of it and then we’re doing the rest of the calculations, does all of the calculations for you, and gives you in radians or degrees. Pretty neat huh? Everystepcalculus dot com. Check out my site and purchase the programs if you want, and enjoy my programs.

Vectors Video

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Raw Transcript

Hey this is tom the calculus and physics guy who programs the TI89 calculators and other calculators for the TI system. uh… today or this video I’m going to be talking about or showing you how how fabulous my programs work on the vectors my site is EveryStepCalculus.com and enjoy my program this is two vectors in space uh… starting from the origin to x_y_z_ uh… points you notice we start again from the index 8 and in the home screen to get to my programs and up comes a menu with all these different types of things that you can compute and we want to do the vectors today so we’re gonna do a-b and vectors we add the first one is it asking for the x_y_z_ point of the first vector uh… vector a again and x_y_z_ and alpha 8 alpha minus seven alpha minus three vector b alpha sixalpha minus five alpha seven shows us what we have if that’s correct and you can go here and press oknow you notice they have the magnitude of vector a choose that one and you can see where the magnitude comes to eleven units uh… shows you how to do it eight squared you know square root of 8 squared minus seven squared minus three squared go back vector B same thing press the this shows you how to do that part uh… a minus b all these different vector calculations come up i wanted to do them when i was in college quickly and not waste time with it and get them exactly accurate vector a minus b is 2 minus b minus 10 if you want to find the magnitude of a minus b you can go a minus b and find that the shows you how to do exactly that putting in the variables dot product and then well move on here got all these different choices A cross product…length B times a cross product B times A there’s a difference uh… constants against a times b times a area of a parallelogram component of A in direction of B equation of a plane all these things cross product is pretty cool ’cause that’s a matrix system and shows you there and then does all the calculations for you and there’s the in the cartesian system i j k system or the vector system with the arrows on the ends of it uh… pretty neat huh enjoy my programs at EveryStepCalculus.com.