Given three vectors a , b and c each two of which are non collinear. Further if (a+b) is collinear with c , ( b + c ) is collinear with a and | a |=| b |=| c |= 2 . Then, the value of | a b + b c + c a | is

Step-by-step solution

Let, a + b = c ...(i) and b+c= a...(ii) Subtracting Eq. (ii) from Eq. (i), array ll & a - c = c - a & (1+ ) a =(1+ ) c array a and c are non-collinear. So, 1+ =0 and 1+ =0 = =-1 Therefore, a + b =- c aligned & a + b + c =0 | a + b + c |^2=0 & | a |^2+| b |^2+| c |^2+2( a b + b c + c a )=0 & 2+2+2+2( b b + b c + c a )=0 & a b + b c + c a =-3 & Hence, | a b + b c + c a |=3 aligned