Given three vectors ` vec a , vec b ,a n d vec c` two of which are non-collinear. Further if `( vec a+ vec b)` is collinear with ` vec c ,( vec b+ vec c)` is collinear with ` vec a ,| vec a|=| vec b|=| vec c|=sqrt(2)dot` Find the value of ` vec a. vec b+ vec b. vec c+ vec c. vec a` a. `3` b. `-3` c. `0` d. cannot be evaluated

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`