Vector A has a magnitude of 3 m and is directed at an angle of 20^ to the X-axis, while vector B has a magnitude of 4 m and is directed at 110^ to the X-axis. Determine their resultant.

Step-by-step solution

The angle between vectors A and B is = 110^ - 20^ = 90^ . Since the vectors are perpendicular, the magnitude of the resultant R is given by: R = A^2 + B^2 = 3^2 + 4^2 = 5 m The angle that the resultant makes with vector A is: = B A = 4 3 = 53^ The angle of the resultant with the X-axis is the sum of the angle of A with the X-axis and the angle : _R = 20^ + 53^ = 73^ Thus, the resultant is 5 m at an angle of 73^ with the X-axis.