Let `vecu,vecv,vecw` be such that `|vecu|=1,|vecv|=2,|vecw|3`. If the projection of `vecv along vecu` is equal to that of `vecw along vecv,vecw` are perpendicular to each other then `|vecu-vecv+vecw|` equals (A) 2 (B) `sqrt(7)` (C) `sqrt(14)` (D) `14`

Options

A. 2
B. `sqrt7`
C. `sqrt14`
D. 14

Answer

c

Explanation

Given `vecv.vecu = vecw .vecu`
`and vecv bot vecw Rightarrow vecv .vecw = 0`
Now, `|vecu - vecu + vecw|^(2)`
` |vecu|^(2) + |vecv|^(2) + |vecw|^(2) = 2vecu.vecv`
` - 2vecw. Vecu + 2vecu .vecw`
1 + 4+ 9
`so |vecu -vecv - vecw|= sqrt14`