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Let vecu, vecv and vecw be vector such t...

Let `vecu, vecv and vecw` be vector such that `vecu+vecv+vecw=vec0`. If `|vecu|=3, |vecv|=4 and |vecw|=5` then `vecu.vecv+vecv.vecw+vecw.vecu` is ………………….. .

A

47

B

`-25`

C

0

D

25

Text Solution

Verified by Experts

The correct Answer is:
b
since `vecu + vecv+vecw=0`, we have
`|vecu + vecv + vecw|^(2) =0`
`or |vecu|^(2)+|vecv|^(2)+|vecw|^(2)+2(vecu.vecv+vecv.vecw+vecw.vecu)`
`or 9 +16+25+2(vecu.vecv +vecv.vecw+vecw.vecu)=0`
`or vecu.vecv + vecv.vecw + vecw.vecu = -25`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -JEE Previous Year (Single Question)
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  2. If veca, vecb, vecc are three non - coplanar vector such that vecaxx(v...

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  3. Let vecu, vecv and vecw be vector such that vecu+vecv+vecw=vec0. If |v...

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  4. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  5. Let vecp,vecq, vecr be three mutually perpendicular vectors of the sam...

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  6. Let veca=2vecj+vecj-2veck,vecb=veci+vecj. If vecc is a vector such tha...

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  7. Let veca = 2i + j+k, vecb = i+ 2j -k and a unit vector vecc be coplana...

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  8. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  9. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  10. If vec a , vec ba n d vec c are unit coplanar vectors, then the sca...

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  11. If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^...

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  12. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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  16. The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hat...

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  17. if veca , vecb and vecc are three non-zero, non- coplanar vectors and ...

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  18. Let veca=hati+2hatj +hatk, vec=hati-hatj+hatk and vecc=hati+hatj-hatk....

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  19. Lelt two non collinear unit vectors hata and hatb form and acute angle...

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  20. If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(ve...

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