First slide

Straight lines in 3D

Question

The equation of the line passing through the point $(a, b, c)$ and parallel to $z -$ axis is

Very Easy

A

$\frac{x - a}{1} = \frac{y - b}{1} = \frac{z - c}{0}$
B

$\frac{x - a}{0} = \frac{y - b}{1} = \frac{z - c}{1}$
C

$\frac{x - a}{1} = \frac{y - b}{0} = \frac{z - c}{0}$
D

$\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$

Solution

The equation of the line passing through the point $(x_{1}, y_{1}, z_{1})$ and parallel to the line whose direction ratios are $⟨ a, b, c ⟩$ is $\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
The direction cosines of $z -$ axis $⟨ 0, 0, 1 ⟩$
Therefore, the equation of the line passing through the point $(a, b, c)$ and parallel to the line whose direction ratio are $⟨ 0, 0, 1 ⟩$ is $\frac{x - a}{0} = \frac{y - b}{0} = \frac{z - c}{1}$

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