Let a , b , c be three vectors such that a is perpendicular to b and b is perpendicular to c . If | a |=2,| b |=3,| c |=5 and | a + b + c |=4 3 , then the angle between a and c is

Step-by-step solution

Given that a b =0, b c =0,| a |=2,| b |=3 aligned & | c |=5 and | a + b + c |=4 3 & Now, | a + b + c |^2=| a |^2+| b |^2+| c |^2+2 a b +2 b c +2 c a & 48=4+9+25+0+0+2| c | a | & 48-38=2.5 .2 = 1 2 = 3 aligned