The conditions under which the vector `vec P + vec Q and vec P - vec Q` will be at right angles to each other is

Options

A. `vec P cdot vec Q =0`
B. `vec P xx vec Q =0`
C. `|P|=|Q|`
D. `vec P cdot vec Q =1`

Answer

C

Explanation

For two vectors to be perpendicular, their dot product should be zero.
`therefore |vec P + vec Q| cdot | vec P - vec Q|=0`
`therefore P^(2) -Q^(2) =0`
`therefore (P+Q) (P-Q) =0" or "P=-Q" or "P=Q.`
Thus |P| = |Q|