```
a (
```**u · v**) = a |**u**| |**v**| cos θ

Further rearrangements lead to:

= | au| |v| cos θ = (au)·v=u·(av)

You may be somewhat fuzzy about how the cosine function behaves. Rather than memorize abstract stuff, visualize the unit circle with its radius projected onto the x-axis. From the picture,

the cosine of 0° = 1.0,

the cosine of 30° = 0.866,

the cosine of 45° = 0.707,

the cosine of 60° = 0.500,

the cosine of 90° = 0.0.

Recall that:

u · v= |u| |v| cos θ

Two vectors are oriented at 90° to each other. What is their dot product?