Let ` vec a , vec b` and ` vec c` be three non-zero vectors such that no two of them are collinear and `( vec axx vec b)xx vec c=1/3|vec c|| vec b| vec a` . If `theta` is the angle between vectors ` vec b` and ` vec c` then a value of `sintheta` is :

Explanation

`( vec a xx vec b ) xx vec c = 1/3 |vec b| | vec c| vec a`

so,`-{(vec c * vec b) vec a - ( vec c * vec a) vec b}= 1/3 | vec b| | vec c| vec a`

`= (vec c* vec a)* vec b - ( vec c * vec b)vec a= 1/3 |vec b| | vec c| vec a`

`= -( vec c * vec b) = 1/3 | vec b ||vec c| `

`= - |vec c||vec b| cos theta = 1/3|vec b||vec c|`

`cos theta = -1/3`

`sin theta = sqrt(1-cos^2 theta)`

`= sqrt(1- 1/9) = sqrt(8/9) = 2 sqrt2/3`

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