Question

The resultant $R$ of $P$ and $Q$ is perpendicular to $P$. Also $|P|=|R|$. The angle between $P$ and $Q$ is $[tan45^{°}=1]$

• A. $\frac{5\pi }{4}$
• B. $\frac{7\pi }{4}$
• C. $\frac{\pi }{4}$
• D. $\frac{3\pi }{4}$

Answer 1

Answer: (D)

Given that $R$ is resultant of $P$ and $Q$ as shown in the figure below, $BC=P,CA=Q$ and $BA=R$

Given, $BA$ and $BC$ are perpendicular and equal in magnitude. So, from property of triangle,
$\angle ACB=45^{\circ }$
Now, $BC$ has to be extended up to $D$ so, that $CD=P$
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 $3\frac{\pi }{4}$.