1.

If veca,vecb,vecc are unit vectors such that veca+vecb+vecc = vec0, find the value of veca.vecb+vecb.vecc+vecc.veca.

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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