Chapter 7, Problem 5OQ

Let $\hat{\text{N}}$ represent the direction horizontally north, $\widehat{\text{NE}}$ represent northeast (halfway between north and east), and so on. Each direction specification can be thought of as a unit vector. Rank from the largest to the smallest the following dot products. Note that zero is larger than a negative number. If two quantities are equal, display that fact in your ranking. (a) $\hat{\text{N}}$ • $\hat{\text{E}}$ (b) $\hat{\text{N}}$ • $\widehat{\text{NE}}$ (c) $\hat{\text{N}}$ • $\hat{\text{S}}$ (d) $\hat{\text{N}}$ • $\hat{\text{E}}$ (e) $\widehat{\text{SE}}$ • S