At the end of this section you should be able to:

1. Convert a 2D vector from polar form to Cartesian component form and vice versa

2. Convert a 3D vector into component form when given its coordinates in

   1. Spherical form

   2. Direction angles

   3. Two points

3. Add together multiple vectors in component form

4. Calculate a unit vector in the direction of a position vector

5. Calculate the dot- and cross-product of two 3D vectors

Learn the vector fundamentals used in every statics free-body diagram and equilibrium setup. You will convert 2D vectors between polar form and Cartesian components, build 3D vectors from spherical coordinates, direction angles, and two-point geometry, then apply vector addition, unit vectors, dot product, and cross product, with Mathematica tools for checking and computation.