Raw Transcript

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.

## Cross Product Example

### Raw Transcript

This video is on cross product. Many people have asked for it and I’m going to do it in my fabulous programs. Press 2nd alpha, to get the letters, enter index, 2nd alpha again and 8 (). So you should have, index 8 () to get to my menu. Go to cross product, press enter. It has for vector A and you press alpha to put anything in the empty lines in all my programs. This is the way the calculator operates. Then we’re gonna press alpha 8, press enter twice, input alpha -6 enter twice, alpha 4 and enter twice. These are for the vector A. For vector B, enter alpha 4, press enter twice, alpha -8 remember the negative sign is different from the minus sign for equations. Enter the y component of the B vector alpha -9 enter twice, z is alpha 4 enter twice. This is what we’ve entered: A = <8., -6., 4.> B = <-8., -9., 4.> Select ok (or change if you want) Now up comes the menu for all vectors and those things we’ll be able to do it. Here we have cross products, A x B cross product which is different from B x A cross product. I do both of them for me and you. Gonna do A x B first. Here are the vectors: A x B (cross product) =

= < 8., -6., 4.,>

X <-8., -9., 4>

Matrix multiplication

= <8., -6., 4.>

<-8., -9., 4.>

Press enter and see the calculations for i,k,j vectors or coordinates

=[(-6.) (4.) – (4.) (-9.)] i –

[(8.) (4.) – (4.) (-8.)] j +

[(8.) (-9.) – (6.) (-8.)] k

Enter and it keeps doing the multiplications

= [(-24.) – (-36.)] i –

[(32.) – (-32.)] j +

[(-72.) – (48.)] k

= 12i – 64j 120k (i,j,k system)

= (vector notation)

Now B x A cross product and here are the calculations

=[(-9.) (4.) –

(4.) (-6.)] i –

[(-8.) (4.) –

(4.) (8.)] j +

[(-8.) (-6.) –

(-9.) (8.)] k

Down on the page, do them all perfect

=[9-36.) – (-24.)] i –

[(-32.) – (32.)] j +

[(48.) – (-72.)] k

= -12.i + 64. J + 120. K

= <-12., 64., 120.>

Pretty neat, everystepcalculus.com, buy my programs you’ll be thrilled.