Let ( p q ) denote the angle between p and q . If a + b + c = 0 , | a | = 7, | b | = 5 and | c | = 3 then (take = 22 7 )

Step-by-step solution

Given a + b + c = 0 , we can write a + c = - b . Squaring both sides, we get: | a |^2 + | c |^2 + 2| a || c | ( a c ) = | b |^2 Substituting the given values | a | = 7 , | b | = 5 , and | c | = 3 : 7^2 + 3^2 + 2(7)(3) ( a c ) = 5^2 49 + 9 + 42 ( a c ) = 25 58 + 42 ( a c ) = 25 42 ( a c ) = -33 ( a c ) = - 33 42 = - 11 14 Given = 22 7 , we can rewrite the expression as: - 11 14 = - 1 4 ( 22 7 ) = - 4 Therefore, ( a c ) = - 4 . Answer: ( a c ) = - 4