Question

If $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$, then the magnitude of $\overrightarrow{B}$ is

• A. $6\sqrt{5}\text{N}$
• B. $3\sqrt{5}\text{N}$
• C. $5\sqrt{5}\text{N}$
• D. $4\sqrt{5}\text{N}$

Answer 1

The correct option is C $5\sqrt{5}\text{N}$

Here in this problem, we are given with magnitude and direction of two vectors.
Also, $\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$
$\Rightarrow \overrightarrow{B}=\overrightarrow{C}-\overrightarrow{A}$

And, the angle between the vectors is ${90}^{\circ }$, so
$|\overrightarrow{B}|=\sqrt{{|\overrightarrow{C}|}^2+{|\overrightarrow{-A}|}^2}=\sqrt{{10}^2+5^2}$
$\Rightarrow |\overrightarrow{B}|=5\sqrt{5}\text{N}$