Question

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

• A. $0^{\circ }$
• B. ${90}^{\circ }$
• C. ${180}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${90}^{\circ }$

Given the magnitude of the resultant is $5$ units,
So, using parallelogram law we have
$R=\sqrt{3^2+4^2+2\times 3\times 4\times \cos \theta }$, where $\theta$ is the angle between the vectors.
$\Rightarrow 5=\sqrt{3^2+4^2+2\times 3\times 4\times \cos \theta }$
Or, $5^2=3^2+4^2+2\times 3\times 4\times \cos \theta$
Or, $25=25+24\cos \theta \Rightarrow \cos \theta =0$
$\Rightarrow \theta ={90}^{\circ }$