Finding nonzero vectors where a × b = a × c but b ≠ c

[Giuseppe]

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

 

[inha]

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

 

[Antiphon]

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]

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.

 

[inha]

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

 

[balakrishnan_v]

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)