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|`.

Answer

1

Explanation

`veca.vecb = 0 Rightarrow veca bot vecb`
`veca .vecc = 0 Rightarrow veca bot vecc`
` Rightarrow veca bot vecb -vecc`
`|veca xx vecb -veca xx vecc|=|veca xx (vecb-vecc)|`
`= |veca||vecb-vecc|=|vecb -vecc|`
Now `|vecb -vecc|^(2) = |vecb|^(2)+|vecc|^(2) -2 |vecb||vecc|cos "" pi/3`
` = 2 -2 x xx 1/2=1 `
`|vecb -vecc|=1`