Determine the sum of vectors A , B , and C , each possessing a magnitude of 100 units and inclined to the X-axis at angles of 45^ , 135^ , and 315^ respectively.

Step-by-step solution

The vectors can be expressed in Cartesian coordinates as follows: A = 100( 45^ i + 45^ j ) B = 100( 135^ i + 135^ j ) = 100(- 45^ i + 45^ j ) C = 100( 315^ i + 315^ j ) = 100( 45^ i - 45^ j ) Observing vectors B and C , their angles differ by 315^ - 135^ = 180^ . Since they have equal magnitudes and are in opposite directions, their sum is zero: B + C = 0 The resultant of the three vectors is: R = A + B + C = A + 0 = A Therefore, the resultant vector is equal to A , which has a magnitude of 100 units and is incline