Let u, v and 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|` is equal to

Options

A. 2
B. `sqrt7`
C. `sqrt(14)`
D. 14

Answer

C

Explanation

Since, `|u| = 1, |v| = 2,|w| = 3`
The projection of v along `u = (v.u)/(|u|)` and the projection of w along `u = (w.u)/(|u|)`.
According to given condition.
`(v.u)/(|u|) = (w.u)/(|u|)`
`rArr v.u = w.u "…."(i)`
Since, v and w are perpendicular to each other.
`:. v. w = 0`
Now, `| u- v + w|^(2) = |u|^(2) + |v|^(2) +|w|^(2)`
`- 2u . v - 2v.w+2u.w`
`rArr |u- b- v + w|^(2) = 1 + 4+ 9 - 2 u . v + 0 + 2u . v` [from Eq. (i) ]
`rArr |u - v + w|^(2) = 1 + 4 + 9`
`:. |u- v + w| = sqrt(14)`