Transcript
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.
Leave a Reply