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Let veca and vecb be two non-collinear u...

Let `veca` and `vecb` be two non-collinear unit vectors. If `vecu=veca-(veca.vecb)vecb` and `vec=vecaxxvecb`, then `|vecv|` is

A

`|vecu|`

B

`|vecu|+ |vecu.vecb|`

C

`|vecu| + |vecu .veca|`

D

none of these

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Verified by Experts

The correct Answer is:
b,d
`vecu = vecas - ( veca . Vecb) vecb`
` vecb xx (veca xx vecb)`
` Rightarrow |vecu| = |vecb xx (veca xx vecb)|`
` |vecb| |veca xx vecb| sin 90 ^(@)`
` |vecb||veca xx vecb|`
` |vecv|`
Also ` vecu . Vecb = vecb.vecb xx (veca xx vecb)`
` [vecb vecb veca xx vecb]`
=0
` Rightarrow |vecv| = |vecu| + |vecu. vecb|`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. veca ,vecb and vecc are unimdular and coplanar. A unit vector vecd is ...

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  2. If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc...

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  3. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

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  4. if veca xx vecb = vecc.vecb xx vecc = veca , " where " vecc ne vec0 t...

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  5. Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a ...

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  6. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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  7. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  8. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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  9. The scalars l and m such that lveca + m vecb =vecc, " where " veca, ve...

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  10. If (veca xxv vecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of...

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  11. A,B C and dD are four points such that vec (AB) = m(2 hati - 6 hatj +...

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  12. If the vectors veca, vecb, vecc are non -coplanar and l,m,n are distin...

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  13. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

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  14. If vectors vecA=2hati+3hatj+4hatk, vecB=hati+hatj+5hatk and vecC form ...

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  15. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= ...

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  16. If veca xx (vecbxx vecc)= (veca xx vecb)xxvecc then

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  17. A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk...

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  18. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

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  19. Statement 1: Vector vecc = -5hati + 7 hatj + 2hatk is along the bisec...

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  20. Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the ...

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