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

Options

A. `pi/6`
B. `pi/4`
C. `pi/3`
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`