Question

If →a and →b are perpendicular vectors |→a+→b|=13 and |→a|=5, find the value of |→b|.

Answer 1

Answer:

$\text{The value of |\vec{b}| is 12}$

Explanation:

Given:

$|\vec{a}|=5\\\\|\vec{a}+\vec{b}|=13$

$\text{since \vec{a} and \vec{b} are perpendicular, }\vec{a}.\vec{b}=0$

We know that,

$|\vec{a}+\vec{b}|^2=|\vec{a}|^2+|\vec{b}|^2+2\,\vec{a}.\vec{b}$

$\implies\;13^2=5^2+|\vec{b}|^2+2(0)$

$\implies\;169=25+|\vec{b}|^2$

$\implies\;|\vec{b}|^2=144$

$\implies\;|\vec{b}|=\sqrt{144}$

$\implies|\vec{b}|=12$