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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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Video Transcript

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 Help Video

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 Calculus Help using ti-89 video transcript

This a video on calculus help, many of you have asked for this, this is the ultimate
calculus help program, uhm, this a video for you if you need help in calculus. The instructions
that go along with my programs is the ultimate cheat sheet for you also. When printed out
you are indexed to all that my programs do and they can do quite a bit. All my menu driven
programs are all step by step, and let’s get started here. You’ll notice index8 here
in the entry line of the calculator and you press second alpha, to put in the, uhm, allows
you to put in the letters and then you press alpha to put in the eight and the closed parenthesis,
open and closed parenthesis. Press enter and your into this program here, which is my menu.
And you scroll up or down on my menu and choose the problem you need calculus help with. For
instance, you have graph by hand, implicit differentiation, inflection point, integrals
algebra, integrate by parts, more graphing by hand, intervals of increase or decrease,
limits. You press the clover leaf scroll down button on your calculator to access all these
programs. Let’s do a quick one here. Let’s do product rule for instance, product rule
is when you see a problem and it has a times sign in between two functions , and uhm, quotient
rule would be if you saw a function or a problem and it had a division sign in it, and here’s
the formula for it. And you can enter, you enter it in these brackets here, you put those
in, you have to press alpha first, so your going to have to put that open parenthesis,
and then you cab put, let’s say four times x and then you close off the bracket and put
the new one in, times, lt’s say , three times x squared plus six and close off the
parenthesis, and press enter, it shows you what you’ve entered, you can change it if
you want, I say it’s ok, and then it does the problem for you, and you put all this
down on your paper, or homework, and here’s the answer thirty six x squared plus twenty-four,
ah pretty neat huh? Every step calculus dot come, check it out, check out my programs
and the blog whatever.

Critical numbers and critical points in graphing

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It seems that most calculus tests I receive to check my programs with, and with regards to graphing a function by hand, they always have you find: ” critical points”.  Then the answer is always just what “x” equals.  You factor the first derivative f ‘(x), find the value of x or x’s and mark it down on your test problem to get it correct x=2 or x=5 or whatever.  If I was your professor (you wish) you’d have gotten only partial credit because you found the “critical numbers” and not the “critical points”.  However, critical points are actually the value of (x,y).  You find the values of x, from the first derivative, plug those values into the original function f(x) to find the value of y, and you have the critical point or points (x,y).  When tests ask for critical numbers the professor actually means critical numbers.  There is a difference!! In my program I find both for you critical numbers and critical points (step by step of course) and leave it up to you as to what or how your professor teaches this, in most cases teaching it incorrectly, what else is new?

Calculus

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I had a person question me over the difference quotient.  He couldn’t load 4x-3 into my programs.  I had not programmed that “straight line” into my programs I had only programmed something with x^2 (curve).  He gave me a you tube video feed that 4x-1 was a valid function.  I guess it is after watching the feed.  So I programmed it for him and now you.  I’m a guy who thinks practical about things.  I programmed my calculator because I was smart and allowed to use the calculator for tests.

 

Point Slope Form: The relation to calculus

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The equation of a line to a point on a curve (point slope form) includes the slope and the position of that line on that curve function.  It’s better than the derivative because the derivative only tells us the slope. Again in Algebra the professor forgot to tell us the importance of that and the relationship to the derivative. Didn’t make it interesting enough to sink in and how it relates to the real world.

You have a function.  Has to have x^2 in it to be a curve from my understanding,  Example y or f(x) = 3x^2

Graph that and you have some form of curve in this case a “valley” parabola, (my own word), -3x^2 and you have a “mountain” parabola (again my own word).

Pick any point “(x,y)” Example: (3,12)

Point = (3,12)

x = 3

y = 12

 Find the derivative:   f(x) = 3x^2

f’(x) = (2)(3)x^(2-1)

= 6x^(1)

= 6x

Compute the derivative at the point “x”

f’(3) = 6(3)

= 18 = m = slope

Point slope form = y = mx + b

y   = 12 so:

 12 = mx + b

m  = 18

12 = 18x + b

x    = 3  so:

12  = 18(3) + b

= 54 + b

b    = 12 – 54

= – 42

y    = mx + b

= 18x + -42

 If you graph this equation along with the original function you’ll see the tangent line to that point on the curve

The slope =  18/1   (rise over run)

The angle of that tangent line = tan^(-1)(18/1) = 86.8 degrees

(make sure your calculator mode is in APPROXIMATE and DEGREES)

Fabulous and exciting, right?  lol Tom

p.s. You’ll love my programs

Have a test or quiz on point slope form? Here is a video example using the programs on the TI-89 calculator: (Click Links below)

Point Slope Form Calculator

Point Slope Form Given Two Points