Question

The magnitude of two vectors P and Q given by R²=P²+Q².what is the angle between them

Answer 1

Hey there!
We know the resultant R is given by
R= root over of P^2+Q^2+2PQcostheta
Hence if theta=90 degree,
Then costheta=0
Thus R^2=P^2+Q^2
And the angle is 90 degree
Hope that helps you ✌️

Answer 2

$\boxed{\begin{minipage}{17em} \text{There are two vectors: \vec{P} and \vec{Q} }\\\\\text{The Resultant Vector is }\vec{R}\\\\\text{Let the angle between \vec{P} and \vec{Q} be }\theta\\\\\\So,\\\\\\\vec{R}=\vec{P}+\vec{Q}\\\\\\\implies R^2=P^2+Q^2+2PQ\cos\theta\\\\\\\text{Given in question that }R^2=P^2+Q^2\\\\\\\implies R^2=R^2+2PQ\cos\theta\\\\\\\implies 0=2PQ\cos\theta\\\\\\\implies\cos\theta=0\\\\\\\implies\boxed{\theta=\frac{\pi}{2}}\\\\\\\textbf{Thus the angle is \frac \pi 2 } \end{minipage}}$