Dot Product Insight

Recall the dot product of 2 vectors is defined to be the value (a)(c) + (b)(d). Note that the dot product of 2 vectors is a scalar quantity. In the applet below two vectors (u and v) are drawn with the same initial point. Their dot product is also shown. Interact with this applet for a few minutes. Do you notice anything (or several things) that seem interesting about the relationship between the dot product and angle between the vectors? If so, discuss with your group.