If ` vec a , vec b and vec c` are non-coplanar unit vectors such that ` vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2))` , then the angle between ` vec a and vec b` is a. `3pi//4` b. `pi//4` c. `pi//2` d. `pi`

Options

A. `3 pi//4`
B. `pi//4`
C. `pi//2`
D. `pi`

Answer

a

Explanation

Since `veca xx (vecb xx vecc) = (vecb + vecc)/ sqrt2`
`(veca.vecc)vecb - (veca.vecb)vecc= 1/sqrt2 vecb+1/sqrt2vecc`
since `vecb and vecc` are non- coplanar,
`Rightarrow veca.vecc=1/sqrt2 and veca. vecb=-1/sqrt2`
`Rightarrow cos theta =-1/sqrt2`
(because `veca and vecb` are unit vectors)
` or theta= (3pi)/4`