General dot product rule

Question

I have a vector $v$ and a scalar $a \in \mathbb{R}$.

let $w = a\overrightarrow{v}$

Then is $\overrightarrow{w} \cdot \overrightarrow{v} = a(\overrightarrow{v} \cdot \overrightarrow{v})$

?

Answer 1

Yes; the dot product is bilinear.