Four dogs named Ang, Bing, Chang, and Dong play a game of tug of war with a toy. Ang pulls on the toy in a direction south of east, Bing in a direction east of north, and Chang in a direction west of north. Ang pulls strongly with a force of magnitude 0.160 kN. Bing pulls even more strongly than Ang with a force of magnitude 0.200 kN, and Chang pulls with a force of magnitude 0.140 kN. When Dong pulls on the toy in such a way that his force is equal in magnitude and opposite in direction to the resultant of the other three forces, the toy does not move in any direction.
What magnitude force does Dong pull on the toy with?
At what angle south of west does Dong pull the toy?
The displacement vector m is added to the displacement vector . The sum of these vectors has a length that is equal to five times the component of . Find .
Three displacement vectors , , and have magnitudes 10.0 m, 7.0 m, and 8.0 m respectively. The directions of , , and make counterclockwise angles of , , and , respectively, with the positive -axis, as shown in the diagram.