If |vector P + vector Q| = |vector P| - |vector P| then the angle between the vectors vector P and vector Q (a) 0° (b) 90°

Question

If  \(|\vec P + \vec Q|\) = \(|\vec P|\) - \(|\vec P|\), then the angle between the vectors \(\vec P\) and \(\vec Q\)

(a) 0° 

(b) 90°

(c) 180° 

(d) 360°

Answer 1

(c) 180°

\(|\vec P + \vec Q|\) = \(|\vec P|\) \(|\vec P|\)

Square on both side, and the resultant becomes 

P² + Q² + 2PQ cos θ = P² + Q² – 2PQ .

cos θ = -1 

θ = 180°