# Vector Cross Product

1. Sep 16, 2007

### noeinstein

1. The problem statement, all variables and given/known data

Given that A = 2i + 4j, evaluate each of the following. (Hint: This question can be answered without computation.)

(a) What is AxB when B = 8i + 16j?

(b) What is AxB when B = -8i - 16j?

2. Relevant equations

AxB=(Axi + Ayj) x (Bxi +Byj)
=(AxBx)(i x i) + (AxBy)(i x j) + (AyBx)(j x i) + (AyBy)(j x j)
AxB=(AxBy - AyBx)k

3. The attempt at a solution

AxB= (2 x 16)k - (4 x 8)k= 0k

2. Sep 16, 2007

### arildno

Indeed.

Can you see the relation between A and B that makes the zero result trivial, i.e you can solve it "without" computation?

3. Sep 16, 2007

### noeinstein

They have the same/opposite direction?

4. Sep 16, 2007

### noeinstein

Geeze no kidding! dahh. Thanks

5. Sep 16, 2007

### arildno

Indeed.
The vectors involved are parallell. Therefore, their cross product must be 0.

6. Sep 16, 2007

### Astronuc

Staff Emeritus
Try parallel or colinear. They are scalar multiples of the same unit vector.