Dot Product Distributes over Addition/Proof 3
Jump to navigation
Jump to search
Theorem
- $\paren {\mathbf u + \mathbf v} \cdot \mathbf w = \mathbf u \cdot \mathbf w + \mathbf v \cdot \mathbf w$
Proof
From Dot Product Operator is Bilinear:
- $\paren {c \mathbf u + \mathbf v} \cdot \mathbf w = c \paren {\mathbf u \cdot \mathbf w} + \paren {\mathbf v \cdot \mathbf w}$
Setting $c = 1$ yields the result.
$\blacksquare$