Find the vector equation of a line passing through the point (1, 3, 4) and parallel to the vector i - j + 2k.

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Q1. The vector equation of a line passing through the point $(1, 3, 4)$ and parallel to the vector $\mathbf{i} - \mathbf{j} + 2\mathbf{k}$ is given by the formula $\mathbf{r} = \mathbf{a} + \lambda \mathbf{b}$, where $\mathbf{a}$ is the position vector of the point and $\mathbf{b}$ is the direction vector.
Given point: $(1, 3, 4) \implies \mathbf{a} = \mathbf{i} + 3\mathbf{j} + 4\mathbf{k}$
Given parallel vector