Resultant of two vectors P and Q is of magnitude A. If Q is reversed, then the resultant is of magnitude B. The value of A^2 + B^2 is

Step-by-step solution

Let the angle between vectors P and Q be . The magnitude of the resultant of P and Q is A . A^2 = P^2 + Q^2 + 2PQ When Q is reversed, the angle between P and - Q becomes 180^ - . The magnitude of the new resultant is B . B^2 = P^2 + Q^2 + 2PQ (180^ - ) B^2 = P^2 + Q^2 - 2PQ Adding the two equations, we get: A^2 + B^2 = (P^2 + Q^2 + 2PQ ) + (P^2 + Q^2 - 2PQ ) A^2 + B^2 = 2(P^2 + Q^2)