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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.
Solution
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
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