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Question
If `veca ≠ vec(0), veca.vecb = veca.vecc, veca xx vecb = veca xx vecc`, then show that `vecb = vecc`.
Solution
We have `veca. (vecb - vecc)` = 0
⇒ `(vecb - vecc) = vec(0)` or `veca ⊥ (vecb - vecc)`
⇒ `vecb = vecc` or `veca ⊥ (vecb - vecc)`
Also `veca xx (vecb - vecc) = vec(0)`
⇒ `(vecb - vecc) = vec(0)` or `veca || (vecb - vecc)`
⇒ `vecb = vecc` or `veca || (vecb - vecc)`
`veca` cannot be both perpendicular to `(vecb - vecc)` and parallel to `(vecb - vecc)`
Hence, `vecb = vecc`.
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