Math 2720: Multiviariable Calculus
Homework #5
Due Monday, January 26
For this homework, you’ll need to remember the Law of Cosines. Suppose
you have a triangle
c
b a
θ with side lengths a, b and c, and the angle opposite the side with length c is
θ; then
c2 = a2 + b2 − 2ab cos(θ).
Problem 1 Suppose you’ve got two points a = (a1 , a2 ) and b = (b1 , b2 ) in
R2 . Together with the origin 0 = (0, 0), they form a triangle.
(a) Apply the Law of Cosines to this triangle and get some kind of
equation involving θ.
(b) Solve the equation for cos(θ) and simplify as much as you can.
Problem 2 Now repeat Problem 1, but use points in Rn instead of R2 .