Question

If $\overrightarrow{a}$ is a unit vector and $\left(\overrightarrow{x}-\hat{a}\right).\left(\overrightarrow{x}+\hat{a}\right)=15$ then find the value of $\left|\overrightarrow{x}\right|$

Answer 1

$\overrightarrow{a}$ is unit vector

$|\overrightarrow{a}|=1$

$(\overrightarrow{x}-\hat{a}).(\overrightarrow{x}+\hat{a})=15$

$|\overrightarrow{x}{|}^2+\hat{a}.\overrightarrow{x}-\hat{a}.\overrightarrow{x}-\hat{a}.\hat{2}=15$
$|\overrightarrow{x}{|}^2-|\overrightarrow{a}{|}^2=15$

$|\overrightarrow{x}{|}^2-1=15$

$|\overrightarrow{x}{|}^2=16$

$|\overrightarrow{x}|=4$