& -2 & 1 \\

February 22, 2026

$& -2 & 1 \\$

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Compute $ \|\mathbf{a}\|^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14 $
Now compute $ \mathbf{a} \times \mathbf{b} $:
\mathbf{a} \times \mathbf{b} = \begin{vmatrix}
\end{vmatrix} = \mathbf{i}(2 \cdot 1 - 3 \cdot (-2)) - \mathbf{j}(1 \cdot 1 - 3 \cdot 1) + \mathbf{k}(1 \cdot (-2) - 2 \cdot 1)
= \mathbf{i}(2 + 6) - \mathbf{j}(1 - 3) + \mathbf{k}(-2 - 2) = \langle 8, 2, -4 \rangle
14\mathbf{v} = \langle 8, 2, -4 \rangle \quad \Rightarrow \quad \mathbf{v} = \frac{1}{14} \langle 8, 2, -4 \rangle = \left\langle \frac{4}{7}, \frac{1}{7}, -\frac{2}{7} \right\rangle

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