]> Exercise 3.5

Exercise 3.5

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.