If A = B + C and magnitudes of A , B and C are 5, 4 and 3 units respectively. The angle between A and C is

Step-by-step solution

Given A = B + C Rearranging the terms, we get: B = A - C Taking the dot product of B with itself: | B |^2 = | A - C |^2 | B |^2 = | A |^2 + | C |^2 - 2| A || C | where is the angle between A and C . Substituting the given magnitudes A = 5 , B = 4 , and C = 3 : 4^2 = 5^2 + 3^2 - 2(5)(3) 16 = 25 + 9 - 30 16 = 34 - 30 30 = 18 = 18 30 = 3 5 = ⁻¹ ( 3 5 ) Answer: ⁻¹ ( 3 / 5 )