# Applications of Vector Dot & Cross Products

Work (in physics) is done whenever a force causes linear displacement. That is to say, work is the amount of force along the displacement vector.

Torque is the turning effect done by a force that causes angular displacement.

Work
$$W = \vec{F}\cdot\vec{d}$$
$$W = \vert\vec{F}\vert\vert\vec{d}\vert\cos{\theta}$$
Unit is $$N\cdot m$$ or Joules
Area of llgm
$$Area = l \cdot w$$
$$Area = \vert\vec{a}\vert\vert\vec{b}\vert\sin{\theta}$$
$$Area = \vert\vec{a} \times \vec{b}\vert$$
Torque
$$\vec{T} = \vec{r} \times \vec{F}$$
$$\vec{T} = \vert\vec{r}\vert\vert\vec{F}\vert\sin{\theta} \text{ } \hat{n}$$
Unit is $$N\cdot m$$ or Joules

Find the area of the triangle with the vertices P(7,2,-5), Q(9,-1,-6), and R(7,3,-3).

A 25kg box is located 8m up a ramp inclined at an angle of 18° to the horizontal. Determine the work done by the force of gravity as the box slides to the bottom of the ramp.

Find the torque produced by a cyclist exterting a force of 115 N on a pedal in the position shown in the diagram, if the shaft of the pedal is 16cm long.