Chapter 10: Q. 60 (page 813)
Let \(θ\) be the angle between nonzero vectors \(u\) and \(v\).
Prove each of the following:
(a) \(θ\) is acute if and only if \(u · v > 0\)
(b) \(θ\) is right if and only if \(u · v = 0\)
(c) \(θ\) is obtuse if and only if \(u · v < 0\)
Short Answer
Part (a) It is proven that \(θ\) is acute if and only if \(u · v > 0\).
Part (b) It is proven that \(θ\) is right if and only if \(u · v = 0\).
Part (c) It is proven that \(θ\) is obtuse if and only if \(u · v < 0\).