Let a , b , c be the unit vectors such that a is perpendicular to b and the angle between b and c is 120^ . If a + c is perpendicular to b + c then

Step-by-step solution

Given | a | = | b | = | c | = 1 a b = 0 b c = | b || c | 120^ = - 1 2 Since a + c is perpendicular to b + c , we have: ( a + c ) ( b + c ) = 0 a b + a c + c b + | c |^2 = 0 0 + a c - 1 2 + 1 = 0 a c = - 1 2 Now, evaluating the expression in the options: ( a - c ) ( b - c ) = a b - a c - c b + | c |^2 = 0 - (- 1 2 ) - (- 1 2 ) + 1 = 1 2 + 1 2 + 1 = 2