Two vectors have magnitudes of 3 unit and 4 unit, respectively. Determine the angle between them if the magnitude of the resultant is 5 unit.

Step-by-step solution

Let the magnitudes of the two vectors be A = 3 unit and B = 4 unit. Let the magnitude of the resultant vector be R = 5 unit. The magnitude of the resultant of two vectors is given by the formula: R^2 = A^2 + B^2 + 2AB Substituting the given values: 5^2 = 3^2 + 4^2 + 2(3)(4) 25 = 9 + 16 + 24 25 = 25 + 24 24 = 0 = 0 = 90^