Question

Let u,v,w be such that |u|=1, |v|=2, |w|=3. If the projection v along u is equal to that of w along u and v, w are perpendicular to each other then |u-v+w| =

• A. 2
• B. 14
• C. $\sqrt{14}$
• D. $\sqrt{7}$

Answer 1

The correct option is C $\sqrt{14}$

Given $\frac{v.v}{|u|}=\frac{w.u}{|u|}\Rightarrow v.u=w.u$.Also given that v. w=0
$|u-v+w{|}^2=|u{|}^2+|v{|}^2+|w{|}^2-2u.v-2v.w+2w.u=|u{|}^2+|v{|}^2+|w{|}^2=1+4+9=14\therefore |u-v+w|=\sqrt{14}$