Let `veca, vecb and vecc` be non-zero vectors such that no two are collinear and `(vecaxxvecb)xxvecc=1/3 |vecb||vecc|veca` if `theta` is the acute angle between vectors `vecb and vecc` then find value of `sin theta`.

Let `veca, vecb and vecc` be non-zero vectors such that no two are col

1.	Let `veca, vecb and vecc` be non-zero vectors such that no two are collinear and `(vecaxxvecb)xxvecc=1/3 \|vecb\|\|vecc\|veca` if `theta` is the acute angle between vectors `vecb and vecc` then find value of `sin theta`.
Answer» we have `(veca xx vecb ) xx vecc = 1/3 \|vecb\|\|vecc\|veca` `or (veca .vecc) vecb - (vecb .vecc)veca = 1/3 \|vecb\|\|vecc\|veca` `or (veca. Vecc) vecb- {(vecb.vecc) + 1/3 \|vecb\|vecc\|} veca =vec0` `Rightarrow veca.vecc =0 and vecb.vecc + 1/3 \|vecb\|vecc\|=0` (`veca and vecb` are non-collinear) or `\|vecb\|\|vecc\|cos theta+ 1/3 \|vecb \|vecc\| =0` `or cos theta = -1//3` `Rightarrow sin theta = sqrt(8/9) = ( 2sqrt2)/3`

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Let `veca, vecb and vecc` be non-zero vectors such that no two are collinear and `(vecaxxvecb)xxvecc=1/3 |vecb||vecc|veca` if `theta` is the acute angle between vectors `vecb and vecc` then find value of `sin theta`.

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