The straigth line x-3 3 = y-2 1 = z-1 0 is: - Vidyadip

MCQ

The straigth line $\frac{\text{x}-3}{3}=\frac{\text{y}-2}{1}=\frac{\text{z}-1}{0}$ is:

A
parallel to $x-$axis
B
parallel to $y-$axis
C
parallel to $z-$axis
✓
perpendicular to $z-$axis

✓

Answer

Correct option: D.

perpendicular to $z-$axis

We have
$\frac{\text{x}-3}{3}=\frac{\text{y}-2}{1}=\frac{\text{z}-1}{0}$
Also, the given line is parallel to the vector $\vec{\text{b}}=3\hat{\text{i}}+\hat{\text{j}}+0\hat{\text{k}}$
Let $\text{x}\hat{\text{i}}+\text{y}\hat{\text{j}}+\text{z}\hat{\text{k}}$ be parpendicular to the given line.
Now,
$3\text{x}+4\text{y}+0\text{z}=0$
It is satisfied by the coordinates of $z-$axis, i.e. $(0, 0, 1).$
Hence, the given line is perpendicular to $z-$axis.

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