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Question
If `veca, vecb, vecc` are three non-zero unequal vectors such that `veca.vecb = veca.vecc`, then find the angle between `veca` and `vecb - vecc`.
Solution
Given, `veca.vecb = veca.vecc`
∴ `veca.vecb - veca.vecc` = 0
`\implies veca.(vecb - vecc)` = 0
Either `vecb = vecc` or `veca ⊥ (vecb - vecc)`
But `vecb ≠ vecc`
[∵ `veca, vecb, vecc` are three non-zero unequal vectors]
∴ Angle between `veca` and `vecb - vecc` is 90°.
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