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  4. The resultant R of P and Q is perpendicular to P. Also | P | = | R |. The angle between P and Q is [tan 45° = 1]

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Q. The resultant $R$ of $P$ and $Q$ is perpendicular to $P$. Also $| P | = | R |$. The angle between $P$ and $Q$ is $[tan\, 45^° = 1]$

MHT CETMHT CET 2019Motion in a Plane

Solution:

Given that $R$ is resultant of $P$ and $Q$ as shown in the figure below, $B C=P, C A=Q$ and $B A=R$
image
Given, $B A$ and $B C$ are perpendicular and equal in magnitude. So, from property of triangle,
$\angle A C B=45^{\circ}$
Now, $B C$ has to be extended up to $D$ so, that $C D = P$
Now, CD and CA have the initial point $C$, so the angle between $CD$ and $CA$;
$=180^{\circ}-45^{\circ}=135^{\circ}=\frac{3 \pi}{4}$
So, angle between $P$ and $Q$ is $3 \frac{\pi}{4}$.