Question

Let $ u,\text{ }v,\text{ }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,\text{ }w $ are perpendicular to each other, then $ |u-v+w| $ equals to

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

Answer 1

Answer: (A)

Given, $ |u|=1,|v|=2|w|=3 $ $ \therefore $ $ \frac{v.u}{|v|}=\frac{w.u}{|u|} $ $ \Rightarrow $ $ v.u=w.u $ and $ u.w=0 $ Now, $ |u-v+w{{|}^{2}}={{u}^{2}}+{{v}^{2}}+{{w}^{2}}-2u.v $ $ +2u.w-2v.w $ $ =1+4+9-2\text{ }v.w=\text{ }14-0=14 $ $ \therefore $ $ |u-v+w|=\sqrt{14} $