If `veca, vecb` and `vecc` are such that `[veca \ vecb \ vecc] =1, vecc= lambda (veca xx vecb)`, angle between `vecc` and `vecb` is `2pi//3`, `|veca|=sqrt2, |vecb|=sqrt3` and `|vecc|=1/sqrt3` then the angle between `veca` and `vecb` is

Options

A. (a) `pi/6`
B. (b) `pi/4`
C. (c) `pi/3`
D. (d) `pi/2`

Answer

b

Explanation

`vecc = lambda (veca xx vecb) `
`or vecc.vecc = lamda (veca xx vecb) .vecc`
` Rightarrow 1/3 = lambda`
Also, `|vecc|^(2) = lamda^(2) |veca xx vecb|^(2) `
` Rightarrow 1/3 = 1/9 (a^(2)b^(2) sin^(2) theta)' = 1/9 xx 2 xx 3sin ^(2) theta`
`or sin theta = 1/2`
`or theta = pi/4`