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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`

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)`

Text Solution

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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