Question

Two vectors of magnitude 3 units and 4 units respectively. What should be the angle between them if the magnitude of the resultant is 5 units ?

• A. ${180}^o$
• B. ${90}^o$
• C. ${45}^o$
• D. ${160}^o$

Answer 1

The correct option is B ${90}^o$

Let the two vectors be $P$ and $Q$ and their resultant vector be $R$.

Let the angle between $P$ and $Q$ be $\theta$.

Given: $|P|=3$, $|Q|=4$ and $|R|=5$ units

Magnitude of resultant vector $|R{|}^2=|P{|}^2+|Q{|}^2+2|P||Q|\cos \theta$

$\therefore$ $5^2=3^2+4^2+2\left(3\right)\left(4\right)\cos \theta$

We get $\cos \theta =0$

$⟹\theta ={90}^o$