Question

Given $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$and the magnitudes of vectors $\overrightarrow{A}$, $\overrightarrow{B}$ and $\overrightarrow{C}$ are respectively 12, 5 and 13 units. The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is

• A. zero
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C

$\frac{\pi }{2}$

If the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\theta$, the magnitude of the resultant is given by
$C^2=A^2+B^2+2ABcos\theta$
$\Rightarrow (13{)}^2=(12{)}^2+(5{)}^2+2\times 12\times 5\times cos\theta$
$\Rightarrow cos\theta =0$
$\Rightarrow \theta =\frac{\pi }{2}$.
Hence, the correct choice is (c).