Suppose the angle between two nonzero vectors A and B is 120^ , and let their resultant be C .

Step-by-step solution

The magnitude of the resultant vector C is given by: C = | A + B | = A^2 + B^2 + 2AB Given = 120^ , 120^ = - 1 2 . Substituting this value: C = A^2 + B^2 - AB The expression for |A - B| can be written as: |A - B| = (A - B)^2 = A^2 + B^2 - 2AB Since A and B are nonzero vectors, their magnitudes A and B are strictly positive, which means AB > 0 . Comparing the terms inside the square roots: A^2 + B^2 - AB > A^2 + B^2 - 2AB Taking the square root of both sides yields: A^2 + B^2 - AB > A^2 + B^2 - 2AB C > |A - B| Thus,