Finding the module and orientation of vector B.

Question

Hello,

I need help with the following question : The vector A = (2x + 3y) m and the sum of the vectors A+B has a magnitude of 4 m orientated at 120 degrees in relation to the x-axis. Calculate the magnitude and the orientation of the vector B.

Thank you.

Answer 1

The components of (A+B) are < 4 cos 120, 4 sin 120 > = < -2, 3.464 >. Vector B = (A+B) - A = < -4, 0.464 >. Therefore the magnitude of B is √ [ (-4)² + (0.464)² ] = 4.027 m.

The orientation angle of B comes from tan^-1 (y/x) = tan^-1 [0.464 / (-4)] = -6.6 or 173.4°. The latter value 173.4° looks correct from a sketch of the situation.