Question

Resultant of `vecP` and `vecQ` is equal to the value of `vecP`.Prove that,resultant of `2vecP` and `vecQ` is perpendicular to `vecQ`?

Answer 1

See below.

Explanation:

If `norm(vec P+vec Q) = norm(vec P)` then

`norm(vecP)^2+2 << vec P, vec Q >> + norm(vec Q)^2 = norm(vec P)^2`

Here `<< cdot, cdot >>` indicates the scalar product of two vectors.

then

`norm (vec Q)^2+2 << vec P, vec Q >> = 0` or

`<< vec Q, 2 vecP + vec Q >> = 0`

so

`vec Q` and `2 vec P+ vec Q` are perpendicular..