# Force Representations

Application of Unit Vector

Force Projection: In some problems, we are interested in finding the projection (component) of a force in a specified direction. Using the eye hook example, let's see how we would find the projection of force vector along line CD as depicted in the figure below.

If the angle α between and line CD is known, then the projection of force along CD is found as

If on the other hand the angle α is not easily available, then we can use a vector operation to solve for . To do this, we must know the unit vector along CD. If there is already a vector along that line, then we can use it to find the desired unit vector as

Then the projection of along line CD is obtained by the dot product

In this case, we can also find angle α as

If we did not have vector , then we would determine the position vector from point C to D. The unit vector is found by dividing by its magnitude.

Example 4 (LiveMath)

Example 5 (LiveMath)

Application of Unit Vector