Given three vectors e`veca, vecb and vecc` two of which are non-collinear. Futrther if `(veca + vecb)` is collinear with `vecc, (vecb +vecc)` is collinear with `veca, |veca|=|vecb|=|vecc|=sqrt2` find the value of `veca. vecb + vecb.vecc+vecc.veca`

Options

A. 3
B. `-3`
C. 0
D. cannot of these

Answer

b

Explanation

` veca + vecb = lambdavecc`
` and vecb + vecc = mu veca`
` ( lambda vecc - veca) = mu veca ("putting" vecb = lambda vecc - veca)`
` Rightarrow ( lambda = mu = -1)`
` Rightarrow veca + vecb + vecc =0`
` or |veca|^(2) + |vecb|^(2) + |vecc|^(2)`
` + 2 (veca .vecb + vecb .vecc + vecc. veca) =0`
` or veca. vecb + vecb . vecc + vecc. veca = -3`