First slide

Straight lines in 3D

Question

The equation of the line passing through the point $(1, 2, 6)$ and parallel to $y -$ axis is

Easy

A

$\frac{x - 0}{1} = \frac{y - 1}{2} = \frac{z - 0}{6}$
B

$\frac{x - 1}{1} = \frac{y - 2}{0} = \frac{z - 6}{1}$
C

$\frac{x - 1}{1} = \frac{y - 2}{1} = \frac{z - 6}{0}$
D

$\frac{x - 1}{0} = \frac{y - 2}{1} = \frac{z - 6}{0}$

Solution

The direction cosines of $y -$ axis $〈0, 1, 0〉$
Therefore, the equation of the line passing through the point $(1, 2, 6)$ nd parallel to the line whose direction ratio are $〈0, 1, 0〉$ is $\frac{x - 1}{0} = \frac{y - 2}{1} = \frac{z - 6}{0}$

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