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Let vecr be a unit vector satisfying vec...

Let `vecr` be a unit vector satisfying `vecr xx veca = vecb, " where " |veca|= sqrt3 and |vecb| = sqrt2`, then

A

`vecr= 2/3(veca+ veca xx vecb)`

B

`vecr= 1/3(veca+ veca xx vecb)`

C

`vecr= 2/3(veca- veca xx vecb)`

D

`vecr= 1/3(-veca+ veca xx vecb)`

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Verified by Experts

The correct Answer is:
b,d
`veca xx (vecr xx veca) = vecaxxvecb`
` 3 vecr - (veca.vecr) veca = veca xx vecb`
Also, `|vecrxxveca|= |vecb|`
`Rightarrow sin^(2)theta= 2/3`
`or (1-cos^(2)theta) = 2/3`
`or 1/3 = cos^(2)theta`
`Rightarrow veca.vecr = +- 1`
`Rightarrow 3 vecr +- veca = veca xx vecb1`
`or vecr = 1/3(vecaxx vecb +- veca)`
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CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercises MCQ
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  8. Let veca vecb and vecc be non- zero vectors aned vecV(1) =veca xx (vec...

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  14. vec a , vec b ,a n d vec c are unimodular and coplanar. A unit vector ...

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

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

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

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