1. Determine the magnitude and direction of the
resultant force R for the two coplanar forces shown.
• Draw the force triangle.
• Use the triangle rule and the Law of Sines and the
Law of Cosines to solve the problem.
Do not resolve the forces into components to find the
2. Determine the magnitude and direction of the
resultant force R for the three coplanar forces
3. Determine the resultant force R for the two 3-D
• List the magnitudes of the components of the
• List the direction cosines for the resultant
• Show both vector forms of the resultant force.
4. The force vector F is given below.
Find the components of the force vector F that
are parallel and perpendicular to the line that
extends from point A to point B. The
coordinates of points A and B are shown in
F = 6 i - 9 j + 3 k kips
5. Four forces (including the weight of the cylinder) are applied to a ring at point A as shown.
Knowing that the system is in equilibrium,
determine the magnitude and direction of the
unknown force T.
Note: The actual direction of T may be
different from that shown in the diagram.
The weight of the cylinder (a vertical force) is 1000 lb.
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