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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 a. `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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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  7. Given three vectors eveca, vecb and vecc two of which are non-collinea...

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  9. If in a right-angled triangle A B C , the hypotenuse A B=p ,t h e n...

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  12. If P is any arbitrary point on the circumcirlce of the equllateral ...

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  13. If vec ra n d vec s are non-zero constant vectors and the scalar b...

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  14. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  15. Given that veca,vecb,vecp,vecq are four vectors such that veca + vecb...

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  16. The position vectors of the vertices A ,Ba n dC of a triangle are t...

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  17. If a is real constant A ,Ba n dC are variable angles and sqrt(a^2-4)ta...

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  19. A non-zero vector vec a is such that its projections along vectors...

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