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 ?

Answer 1

Since we know that,

$|\overrightarrow{\text{R}}{|}^2=|\overrightarrow{\text{A}}{|}^2+|\overrightarrow{\text{B}}{|}^2+2|\overrightarrow{A}|\overrightarrow{B}|\cos \theta$

Given: $|\overrightarrow{\text{R}}|=5;|\overrightarrow{\text{A}}|=3;|\overrightarrow{\text{B}}|=4$

Using these value in formula, we get

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

$25=25+2\left(3\right)\left(4\right)\cos \theta$

$0=2\left(3\right)\left(4\right)\cos \theta$

$0=\cos \theta$

$\Rightarrow \theta ={90}^{\circ }$

$\therefore$ The angle between them is ${90}^{\circ }$.

Hence, option $\left(\text{D}\right)$ is the right.