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Suppose we have two arrows. Let us define the cross product of these two arrows to be a third arrow. The arrow representing the cross product is always exactly 90 degrees to the two original arrows. The length of the arrow representing the cross product is always exactly equal to the area of the parallelogram that is formed by the original two arrows. The cross product of two arrows plays a critical role in many areas of science and engineering. Another type of calculation that plays a critical role is what we refer to as the dot product of two arrows. The first arrow defines a line. This line and the second arrow form a triangle. Consider the length of this side of the triangle. Now, consider this length multiplied by the length of the first arrow. The result of this multiplication is what we refer to as the dot product. If the first arrow and the red arrow are pointed in opposite directions, then the dot product is negative. Whereas the cross product of two arrows is another arrow,