Find parametric equations of the line that passes through the points A (2, 4, −3) and B (3, −1, 1).

Correct option is C

​$$\begin{aligned}&\text{The direction vector } \vec{v} \text{ of the line is obtained by subtracting the coordinates of point } A \text{ from point } B: \\&\vec{v} = \vec{AB} = B - A = (3 - 2, -1 - 4, 1 - (-3)) = (1, -5, 4) \\\\&\textbf{Write the Parametric Equations} \\&\text{Using the coordinates of point } A \text{ and the direction vector } \vec{v}, \text{ the parametric equations of the line are:} \\&\left\{\begin{aligned}x &= 2 + 1 \cdot t \\y &= 4 + (-5) \cdot t \\z &= -3 + 4 \cdot t\end{aligned}\right. \\&\text{where } t \text{ is a parameter that can take any real value.} \\\\&\textbf{Simplified Parametric Equations} \\&\left\{\begin{aligned}x &= 2 + t \\y &= 4 - 5t \\z &= -3 + 4t\end{aligned}\right.\end{aligned}$$​​