# Cross Product of Vectors

1. Dec 14, 2013

### cp255

True or False, if AxB = AxC then either A=0 or B=C.

A, B, and C are vectors and I thought this statement would be true. However the answer key says it is not. Why?

2. Dec 14, 2013

### bhanesh

This can be explained by following example

3. Dec 14, 2013

### cp255

Ok that makes sense. Now if the the magnitude of the cross product was not zero then B would have to equal C Right?

4. Dec 14, 2013

### Staff: Mentor

The magnitude of AxB is equal to the magnitude of A times the magnitude of B times the sine of the angle between the vectors A and B. If the magnitude of C is larger than the magnitude of B, but the sine of the angle between A and C is less, AxC can be equal to AxB.

5. Dec 14, 2013

### D H

Staff Emeritus
Not at all. All that AxB=AxC says is that either A=0 (in which case any two vectors B and C satisfy AxB=AxC), or that the components of B and C normal to A are equal.

6. Dec 14, 2013

### Dick

Or that since AxB=AxC is the same as AxB-AxC=Ax(B-C)=0 then A and B-C are parallel.

Last edited: Dec 14, 2013