First slide

Straight lines in 3D

Question

The equation of a line passing through the point $(1, 1, 1)$ and parallel to $y z -$ plane is

Easy

A

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

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

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

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

Solution

The direction cosines of any line parallel to the $y z -$ plane is $〈0, 1, 1〉$
Therefore, the equation of the line passing through the point $(1, 1, 1)$ and parallel to the line whose direction ratio are $〈0, 1, 1〉$ is $\frac{x - 1}{0} = \frac{y - 1}{1} = \frac{z - 1}{1}$

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