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)`

Options

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)`

Answer

b,d

Explanation

`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)`