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प्रश्न
If `veca, vecb, vecc` are three vectors such that `veca.vecb = veca.vecc` and `veca xx vecb = veca xx vecc, veca ≠ 0`, then show that `vecb = vecc`.
उत्तर
Given, `veca.vecb = veca.vecc`
⇒ `veca.vecb - veca.vecc` = 0
⇒ `veca.(vecb - vecc)` = 0
⇒ Either `vecb = vecc` or `veca ⊥ (vecb - vecc)`
Also, given `veca xx vecb - veca xx vecc`
⇒ `veca xx vecb - veca xx vecc` = 0
⇒ `veca xx (vecb - vecc)` = 0
⇒ Either `veca || (vecb - vecc)` or `vecb = vecc`
But vector `veca` a cannot be both parallel and perpendicular to vector `(vecb - vecc)`.
Hence, vector `vecb = vecc`.
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