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Let vec(a) , vec(b) and vec(c) be three ...

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

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We are given that
`(vec(a)**vec(b))**vec(c) = (1/3)|vec(b)||vec(c)|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)`
Now, as all of them are non-collinear, `(vec(c)*vec(a))` can be `0` that means,
`(vec(c).vec(b)) = (-1/3)|vec(b)||vec(c)|`
`=>|vec(b)||vec(c)|costheta = (-1/3)|vec(b)||vec(c)|`
`=>costheta = -1/3`
...
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