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If vec a , vec b , and vec c be non-ze...

If ` vec a , vec b , and vec c` be non-zero vectors such that no two are collinear or `( vec axx vec b)xx vec c=1/3| vec b|| vec c| vec adot` If `theta` is the acute angle between vectors ` vec b and vecc` , then find the value of `sin thetadot`

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`( 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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