Question

If `veca xx vecb = veca xx vecc` where `veca, vecb` and `vecc` are non-zero vectors, then prove that either `vecb = vecc` or `veca` and `(vecb - vecc)` are parallel.

Answer 1

Given, `veca xx vecb = veca xx vecc`

`\implies veca xx vecb - veca xx vecc = 0`

`\implies veca xx (vecb - vecc) = 0`

Then, `vecb - vecc = 0`, because `veca` is a non-zero vector and the cross-product of two vectors is zero when their angle is 0° i.e., they are parallel to each other.

or `veca` and `(vecb - vecc)` are parallel.

Hence proved