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In space, consider the lines \(d_1\) and \(d_2\) defined by the following parametric representations (\(t, s \in \mathbb{R}\)):$$ d_1 : \begin{cases} x = 1 + t \\ y = -2 + 2t \\ z = 3 - t \end{cases} \quad \text{and} \quad\, d_2 : \begin{cases} x = -1 + 2s \\ y = 4 + s \\ z = 5s \end{cases} $$Determine whether the lines \(d_1\) and \(d_2\) are orthogonal.
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