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If veca,vecb,vecc are unit vectors such that veca+vecb+vecc = vec0, find the value of veca.vecb+vecb.vecc+vecc.veca. |
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Answer» Solution :`veca+vecb+vecc` = 0 `IMPLIES(veca+vecb+vecc)^2` = 0 `|veca|^2+|vecb|^2+|vecc|^2 + 2(veca.vecb+vecb.vecc+vecc.veca)` = 0 `implies 2(veca.vecb+vecb.vecc+vecc.veca)` = -(1+1+1) `(THEREFORE |veca|^2` = `|vecb|^2` = `|vecc|^2` =1 `implies veca.vecb+vecb.vecc+vecc.veca` = -3/2. |
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