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`.

Answer 1

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°.