Let a , b , c be unit vectors such that a is perpendicular to the plane of b and c . If the angle between b and c is 3 , then | a + b + c | =

Step-by-step solution

Given | a | = | b | = | c | = 1 Since a is perpendicular to the plane of b and c , a b = 0 and a c = 0 The angle between b and c is 3 , so b c = | b || c | ( 3 ) = 1 2 We know that | a + b + c |^2 = | a |^2 + | b |^2 + | c |^2 + 2( a b + b c + c a ) Substituting the values: | a + b + c |^2 = 1 + 1 + 1 + 2 (0 + 1 2 + 0 ) | a + b + c |^2 = 3 + 1 = 4 | a + b + c | = 2 Answer: 2