Consider two vectors A and B , each having a magnitude of 10 unit. If these vectors are inclined to the X-axis at angles of 30^ and 60^ respectively, determine their resultant.

Step-by-step solution

Given | A | = 10 and | B | = 10 Angle of A with the X-axis is 30^ and angle of B with the X-axis is 60^ . The angle between the two vectors is = 60^ - 30^ = 30^ . The magnitude of the resultant R is given by: R = A^2 + B^2 + 2AB R = 10^2 + 10^2 + 2(10)(10) 30^ R = 200(1 + 30^ ) Using the identity 1 + = 2 ^2 ( 2 ) : R = 200 (2 ^2 15^ ) = 400 ^2 15^ = 20 15^ Since the magnitudes of both vectors are equal, their resultant bisects the angle between them. Angle of the resultant with the X-axis is 30^ + 30^ 2 = 45^ .