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  • Let a,b and c be non zero vectors such that (a cross b)cross c=1/3 |b||c| a. if theta is an angle between the vectors b and c, then sin theta equals

Let a,b and c be non zero vectors such that (a cross b)cross c=1/3 |b||c| a. if theta is an angle between the vectors b and c, then sin theta equals

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 Solution:

ecause (a imes b) imes c=1/3left | b ight |left | c ight |aRightarrow (acdot c)b-(bcdot c)a=1/3left | b ight |left | c ight |a\ \Rightarrow (acdot c)b=[(bcdot c)+1/3left | b ight |]left | c ight |a\ \Rightarrow (acdot c)b=left | b ight |left | c ight |[cos heta +1]a

As a and b are not parallel acdot c=0;and;cos heta +1/3=0

\Rightarrow cos heta =-1/3Rightarrow sin heta =2sqrt2/3

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Deependra Verma

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