Question 1301a

Vectors II: Lines and Planes

Vector Equation of a Line I

Question

Find the equation of the line passing through the point

{P \left( 5, 1, - 3 \right)}

and parallel to the vector

{\begin{pmatrix} - 1 \\ - 4 \\ 5 \end{pmatrix}.}

{l: }

{\mathbf{r}=\mathbf{a}+\lambda\mathbf{d}, \; \lambda \in \mathbb{R}.}

{\mathbf{a}=}

{\Biggl(}

{\Biggr), \quad}

{\mathbf{d}=}

{\Biggl(}

{\Biggr)}