Question

Find $|\overrightarrow{x}|$ if for a unit vector $\overrightarrow{a},(\overrightarrow{x}-\overrightarrow{a}).(\overrightarrow{x}+\overrightarrow{a})=15.$

Answer 1

Given: $\left|\overrightarrow{a}\right|=1$

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

We know that $(a-b)(a+b)=a^2-b^2$

So, ${\left|\overrightarrow{x}\right|}^2-{\left|\overrightarrow{a}\right|}^2=15$

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

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

$\left|\overrightarrow{x}\right|=4$