Question

The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$ is
(a) parallel to x-axis
(b) parallel to y-axis
(c) parallel to z-axis
(d) perpendicular to z-axis

Answer 1

(d) perpendicular to z-axis

We have

$\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$

Also, the given line is parallel to the vector $\overrightarrow{b}=3\hat{i}+\hat{j}+0\hat{k}$.

Let $x\hat{i}+y\hat{j}+z\hat{k}$ be perpendicular to the given line.

Now,
$3x+4y+0z=0$
It is satisfied by the coordinates of z-axis, i.e. (0, 0, 1).

Hence, the given line is perpendicular to z-axis.