Two vectors have magnitudes of 3 unit and 4 unit, respectively. Determine the angle between them if the magnitude of the resultant is 7 unit.

Step-by-step solution

Let the two vectors be A and B with magnitudes A = 3 and B = 4 . The magnitude of the resultant vector is given by R = A^2 + B^2 + 2AB , where is the angle between the vectors. Given R = 7 , squaring both sides gives: R^2 = A^2 + B^2 + 2AB 7^2 = 3^2 + 4^2 + 2(3)(4) 49 = 9 + 16 + 24 49 = 25 + 24 24 = 24 = 1 = 0^