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Let veca, vecb and vecc be non...

# 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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Updated On: 30-1-2020

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Solution :
we have (veca xx vecb ) xx vecc = 1/3 |vecb||vecc|veca <br> or (veca .vecc) vecb - (vecb .vecc)veca = 1/3 |vecb||vecc|veca <br> or (veca. Vecc) vecb- {(vecb.vecc) + 1/3 |vecb|vecc|} veca =vec0 <br> Rightarrow veca.vecc =0 and vecb.vecc + 1/3 |vecb|vecc|=0 <br> (veca and vecb are non-collinear) <br> or |vecb||vecc|cos theta+ 1/3 |vecb |vecc| =0 <br> or cos theta = -1//3 <br> Rightarrow sin theta = sqrt(8/9) = ( 2sqrt2)/3

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