# Vector help

Hello, can anyone guide me with this problem?

Find nonzero vectors a ,b , and c such that a x b = a x c but b does not equal c

I would appreciate any help. Thanks

## Answers and Replies

The cross product is zero for perpendicular vectors so the cartesian unit vectors would satisfy that as i x j = i x k =0.

inha said:
The cross product is zero for perpendicular vectors so the cartesian unit vectors would satisfy that as i x j = i x k =0.
That's all wrong. The dot product is zero for perpendicular vectors.
The cross product is i x j = k.

LeonhardEuler
Gold Member
Antiphon said:
That's all wrong. The dot product is zero for perpendicular vectors.
The cross product is i x j = k.
Yeah, the cross product is zero for parallel vectors. So (1,1,1) x (2,2,2)= (1,1,1) x (3,3,3) = (0,0,0) is a solution.

Oh hell. I got my products mixed. Scratch that advice and sorry if I caused any problems.

We just need that c=b+ka so that c-b is parallel to a
(a,b,b+ka) satisfies the prop(k is a scalar not equal to zero)