InterviewSolution
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InterviewSolution
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Let ` vec u , vec va n d vec w`be such that `| vec u|=1,| vec v|=2a n d| vec w|=3.`If the projection of ` vec v`along ` vec u`is equal to that of ` vec w`along ` vec u`and vectors ` vec va n d vec w`are perpendicular to eachother, then `| vec u- vec v+ vec w|`equals`2`b. `sqrt(7)`c. `sqrt(14)`d. `14`A. 2B. `sqrt7`C. `sqrt(14)`D. 14 |
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Answer» Correct Answer - C 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)` |
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