Dot Product Insight

Recall the dot product of 2 vectors <a, b> & <c, d> 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? Do you notice any patterns? If so, describe.

Quick (Silent) Demo