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

Here are the solutions to the questions:

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.

Step 1: Identify the position vector $\mathbf{a}$ and the direction vector $\mathbf{b}$.
The point is $(1, 3, 4)$, so $\mathbf{a} = \mathbf{i