Home  18.013A  Chapter 3  Section 3.3 


Write out (v  w)(v  w) using the linearity of the dot product in each of its arguments. What famous law does this establish?
Solution:
The square of the length of (v  w), which is (v  w, v  w) can be expanded to (v, v) + (w, w)  2(v, w) which is the square of the length of v plus the square of the length of w minus twice the length of v times the length of w times the cosine of the angle between them. This is the law of cosines.
