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If a particle located at a point [math]P[/math] is simultaneously acted on by two forces [math]\vec u[/math] and [math]\vec v[/math], then the resultant force is the vector sum [math]\vec u + \vec v[/math]. The fact that vectors are added geometrically by constructing a parallelogram implies a corresponding Parallelogram Law of Forces. Suppose that a particle at the point [math](1,1)[/math] is simultaneously acted on by a force [math]\vec v[/math] of [math]10[/math] pounds in the direction of [math]\frac\pi6[/math] radians and a force [math]\vec u[/math] of [math]\sqrt{32}[/math] pounds in the direction of [math]-\frac\pi4[/math] radians.

• Draw the parallelogram of forces, and show the resultant force.
• What are the coordinates of the resultant force on the particle?