Question 1304b

Vectors II: Lines and Planes

Equation of a Plane from Direction Vectors

Question

The planes

{p_1}

and

{p_2}

are given by

\begin{align*} &p_1: \mathbf{r} \cdot \begin{pmatrix} 1 \\ 2 \\ 0 \end{pmatrix} = 5,\\ &p_2: \mathbf{r} \cdot \begin{pmatrix} - 1 \\ 3 \\ 4 \end{pmatrix} = 1. \end{align*}

Find the equation of the line of intersection,

{l,}

between the two planes.

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

{\mathbf{a}=}

{\Biggl(}

{\Biggr), \quad}

{\mathbf{d}=}

{\Biggl(}

{\Biggr)}