Finding AxB when B is a scalar multiple of A

[noeinstein]

Homework Statement

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?

Homework 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

The Attempt at a Solution

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

 

[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?

 

[noeinstein]

They have the same/opposite direction?

 

[noeinstein]

Geeze no kidding! dahh. Thanks

 

[arildno]

They have the same/opposite direction?

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

 

[Astronuc]

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