The vectors given are $\mathbf{v} = \mathbf{i}$ and $\mathbf{w} = -3 \mathbf{j}$. In component form, $\mathbf{v} = (1, 0)$ and $\mathbf{w} = (0, -3)$.
The dot product is calculated as:
\[
\mathbf{v} \cdot \mathbf{w} = (1, 0) \cdot (0, -3) = 1 \times 0 + 0 \times
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