InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
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 |
|
Answer» 2 The projectionof v ALONG `u = (v.u)/(|u|)` and theprojectionof w along `u = (w.u)/(|u|)`. ACCORDINGTO givencondition. `(v.u)/(|u|) = (w.u)/(|u|)` `rArr v.u = w.u "…."(i)` Since, v and w are perpendicularto 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)` |
|