Chapter 9, Problem 53RE

To determine

To find : The parametric equation that crosses the $x$ axis and $z$ axis at given points.

Explanation of Solution

Given: The equation crosses the $x$ axis at $x=2$ and the $z$ axis $z=-4$ .

A line passing through the point $P\left(x_0,y_0,z_0\right)$ and parallel to the vector $v=\langle a,b,c\rangle$ is described by the equations,

$\begin{array}{l}x=x_0+at\\ y=y_0+bt\\ z=z_0+ct\end{array}$

The points are $P\left(2,0,0\right)$ and $Q\left(0,0,-4\right)$ .

The vector $v$ can be calculated as,

$\begin{array}{c}v=PQ\\ =Q-P\\ =\langle -2,0,-4\rangle \end{array}$

Thus, the parametric equations are,

$\begin{array}{c}x=2-2t\\ y=0\\ z=-4t\end{array}$

Therefore, the parametric equations are listed above.