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If veca,vecb,vecc are mutually perpendic...

If `veca,vecb,vecc` are mutually perpendicular vector and`veca=alpha(vecaxxvecb)+beta(vecbxxvecc)+gamma(veccxxveca) and [veca vecb vecc]=1`, then `alpha+beta+gamma=` (A) `|veca|^2` (B) `-|veca|^2` (C) 0 (D) none of these

Text Solution

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Taking dot poduct with `veca ,vecb and vecc` , respectively we get
`|veca|^(2)=beta.[vecavecbvecc]=beta`
`0=gamma.[veca vecbvecc]=gamma`
` and 0=alpha.[veca vecbvecc]=alpha`
`alpha+beta+gamma=|veca|^(2)`
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