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= 5 \cdot \sqrt{5} \cdot \cos \theta
= \mathbf{i}(6 - 4) - \mathbf{j}(-4 - 1) + \mathbf{k}(8 + 3)
= \mathbf{i}(2) + \mathbf{j}(5) + \mathbf{k}(11)
= \begin{pmatrix} 2 \\ 5 \\ 11 \end{pmatrix}
= \mathbf{i}(2 \cdot 4 - (-1) \cdot 1) - \mathbf{j}(1 \cdot 4 - (-1)(-2)) + \mathbf{k}(1 \cdot 1 - 2 \cdot (-2))
= \mathbf{i}(8 + 1) - \mathbf{j}(4 - 2) + \mathbf{k}(1 + 4)
= 9\mathbf{i} - 2\mathbf{j} + 5\mathbf{k} = \begin{pmatrix} 9 \\ -2 \\ 5 \end{pmatrix}