Given three vectors a , b , c , two of which are collinear. If a + b is collinear with c and b + c is collinear with | a |=| b |=| c |= 2 , then a b + b c + c a =

Step-by-step solution

aligned & a + b = c (i) and b + c = a (i i) & a - c = c - a form (i) and (ii) & (1+ ) a =(1+ ) c & = =-1 & a + b + c =0 & | a + b + c |^2=| a |^2+| b |^2+| c |^2+2( a b + b c + c a ) & 0=2+2+2+2( a b + b c + c a ) & a b + b c + c a =-3 aligned