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Let veca, vecb, vecc be three unit vecto...

Let `veca, vecb, vecc` be three unit vectors and `veca.vecb=veca.vecc=0` . If the angle between `vecb and vecc` is `pi/3` then find the value of `|[veca vecb vecc]|`

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`veca.vecb=veca. Vecc=0`
is perpendicular to vectors `vecb and vecc`. Thus
`veca=lambda(vecbxxvecc)`
`|veca|=|lambda(vecbxxvecc)=|lambdasqrt3/2|=1`
` |[veca vecbvecc]|=|veca.(vecbxxvecc)|`
`=|lambda||(vecbxxvecc)|^(2)`
`=2/sqrt3|vecb|^(2)|vecc|^(2)sin^(2)(pi/3)=2/sqrt3xx(sqrt3/2)^(2)=sqrt3/2`
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