Chapter 11.4, Problem 40E

To determine

To find : a set of parametric equations of the line.

Answer to Problem 40E

  $x=-4,y=5+t,z=2$

Explanation of Solution

Given planes: Line passes through (-4,5,2) and is parallel to xy -plane and the yz -plane.

Calculation:

The line is parallel to both xy -plane and the yz -plane , so it is parallel to the intersection of the two planes , that is y -axis. Therefore, line is parallel to the direction vector $\langle 0,1,0\rangle$ .

We know that the parametric equation of a line through the point $\left(x_0,y_0,z_0\right)$ and parallel to the direction vector $\langle a,b,c\rangle$ is

  $x=x_0+at,y=y_0+bt,z=z_0+ct$

Therefore, equation of line that passes through (2,3,4) and is parallel to xz -plane and the yz -plane is

  $\begin{array}{l}x=-4+0t,y=5+t,z=2+0t\\ x=-4,y=5+t,z=2\end{array}$