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

You may be somewhat fuzzy about how the cosine function behaves. Rather than memorize abstract stuff, I prefer to 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