If $\overline{a},\overline{b}\&\overline{c}$ are vectors such that $\left|\overline{a}\right|=\left|\frac{\overline{b}}{2}\right|=\left|\frac{\overline{c}}{3}\right|=1. \overline{b}\&\overline{c}$ are perpendicular, and projections of $\overline{b}\&\overline{c}$ on $\overline{a}$ are equal then $|\overline{a}-\overline{b}+\overline{c}|=$ 

$\left|\overline{a}\right|=1,\left|\overline{b}\right|=2,\left|\overline{c}\right|=3\&\overline{b}.\overline{c}=0.$

Projection of  $\overline{b}on\overline{a}=$ projection of  $\overline{c}on\overline{a}$

$\frac{\overline{b}.\overline{a}}{\left|\overline{a}\right|}=\frac{\overline{c}.\overline{a}}{\left|\overline{a}\right|}\Rightarrow \overline{b}.\overline{a}=\overline{c}.\overline{a}$

${|\overline{a}-\overline{b}+\overline{c}|}^2={\left|\overline{a}\right|}^2+{\left|\overline{b}\right|}^2+{\left|\overline{c}\right|}^2-2\overline{a}.\overline{b}-2\overline{b}.\overline{c}+2\overline{a}.\overline{c}=1+4+9=14.$