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Let vec u , vec va n d vec w be such th...

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 each other, then `| vec u- vec v+ vec w|` equals `2` b. `sqrt(7)` c. `sqrt(14)` d. `14`

A

2

B

`sqrt7`

C

`sqrt14`

D

14

Text Solution

Verified by Experts

The correct Answer is:
c
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`
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