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Let veca,vecb,vecc be unit vectors such ...

Let `veca,vecb,vecc` be unit vectors such that `veca.vecb=veca.vecc=0` and the angle between `vecb` and `vecc` is `(pi)/(3).` Prove that `veca=+-(2)/(sqrt(3))(vecbxxvecc).`

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We have `veca.vecb = veca .vecb =0`
This implies that `veca` is perpenedicular to both `vecb and vecc`. Thus, `veca` is a unit vector, perpendicular to both `vecb and vecc`.Hence,
`vecr = +-(vecb xx vecc)/(|vecbxxvecc|) = +-(vecbxxvecc)/(|vecb||vecc|sinpi//3)`
` = +- 2 (vecb xx vecc)`
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