First slide

Straight lines in 3D

Question

Equation of line parallel to the line $x = y = z$ and passing through the point $(1, 0, 0)$ is

Moderate

A

$\frac{x - 1}{1} = \frac{y - 1}{1} = \frac{z - 1}{1}$
B

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

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

$\frac{x - 1}{1} = \frac{y}{1} = \frac{z}{1}$

Solution

The equation of the line passing through the point $(x_{1}, y_{1}, z_{1})$ and parallel to the line $\frac{x - x_{2}}{a} = \frac{y - y_{2}}{b} = \frac{z - z_{2}}{c}$ is $\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
Here the given point is $(1, 0, 0)$ and the equation of the line is $x = y = z$
Therefore, the equation of the required line is $\frac{x - 1}{1} = \frac{y - 0}{1} = \frac{z - 0}{1}$

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