Directions: On this worksheet we will be investigating the properties of dot products of two vectors. There are two principle ways to calculate the scalar dot product, AB, of two vectors. As the name implies, it is important to notice that the dot product of two vectors does NOT produce a new vector; instead it results in a scalar - that is, a value that only has magnitude or size, not direction. These methods are:

• AB = |A| |B| cosq
  
  |A| and |B| represent the magnitudes of vectors A and B, while q is the size of the angle between them when placed tail-to-tail
  
  
• AB = A_xB_x + A_yB_y
  
  A_x and B_x represent the horizontal components of vectors A and B, while A_y and B_y represent their vertical components

The example vectors displayed in the table below are not drawn to scale; however, they do indicate correct relative directions.