If `veca and vecb` are any two vectors of magnitudes 1and 2. respectively, and `(1-3veca.vecb)^(2)+|2veca+vecb+3(vecaxxvecb)|^(2)=47` then the angle between `veca and vecb ` is

Options

A. `pi//3`
B. `pi-cos^(-1) (1//4)`
C. `(2pi)/3`
D. `cos^(-1) (1//4)`

Answer

c

Explanation

` 1 + 9 (veca .vecb)^(2) - 6( veca .vecb) + 4 |veca|^(2)`
`+ |vecb|^(2) + 9 |veca xx vecb|^(2) + 4veca.vecb = 47`
`or 1 + 4+4 +36 - 4 cos theta = 47`
`or cos theta = -1/2`
Hence, the angle between `veca and vecb is (2pi)/3`