Chapter 10, Problem 17CRP

Program Description Answer

Lines normal to the surface:

The plane formed by the vertices $\left(1,0,0\right)$, $\left(1,1,1\right)$ and $\left(1,0,2\right)$ is parallel to $yz$-plane because $x$- coordinate is same in all points and only $y$ and $z$ vary. As the plane lies in the $yz$ plane, the normal to the plane is parallel to the $x$-axis.

For the lines to be parallel to the $x$-axis, only $x$-coordinate should change in the points connecting the line and $y$ and $z$-coordinates of the points of the line have to remain same.

The lines which are parallel to $x$-axis are:

• The line segment from $\left(1,1,1\right)\text{to}\left(2,1,1\right)$.
• The line segment from $\left(1,0,2\right)\text{to}\left(0,0,2\right)$.

Hence, the correct answers are option “b” and “c”.