Chapter 11.4, Problem 44E

To determine

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

Answer to Problem 44E

  $x=-4-t,y=5+2t,z=2+t$

Explanation of Solution

Given planes: Line passes through (-4,5,2) and is perpendicular to $-x+2y+z=5$

Calculation:

The normal vector to the plane $-x+2y+z=5$ is $\langle -1,2,1\rangle$ .

Since the line is perpendicular to the plane $3x+2y-z=6$ , so it is parallel to the direction vector $\langle 3,2,-1\rangle$ .

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 (-4,5,2) and is perpendicular to $-x+2y+z=5$ is

  $x=-4-t,y=5+2t,z=2+t$