If ` vec a , vec b , vec c` are unit vectors such that ` vec a. vec b=0= vec a. vec c` and the angle between ` vec b` and `vec c` is `pi/3,` then find the value of `| vec axx vec b- vec axx vec c|`.

Options

A. `1//2`
B. 1
C. 2
D. none of these

Answer

b

Explanation

`|vecaxxvecb-vecaxxvecc|^(2)=|vecaxx(vecb-vecc)|^(2)`
`|veca|^(2)|vecb-vecc|^(2)`
`-(veca.(vecb-vecc))^(2)=|vecb-vecc|^(2)`
`= |vecb|^(2)+|vecc|^92)-2|vecb||vecc|cos (pi/3)=1`