Question 1301b

Vectors II: Lines and Planes

Vector Equation of a Line II

Question

Find the equation of the line that is parallel to

l_2: \mathbf{r} = \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix} + \mu \begin{pmatrix} 2 \\ 1 \\ 2 \end{pmatrix}, \; \mu \in \mathbb{R}

and passes through the point

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

{l: }

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

{\mathbf{a}=}

{\Biggl(}

{\Biggr), \quad}

{\mathbf{d}=}

{\Biggl(}

{\Biggr)}