First slide

Straight lines in 3D

Question

The equation of a line passing through the point on $x -$ axis at a distance of 3 units from the origin and parallel to $x y -$ plane is

Easy

A

$\frac{x - 3}{1} = \frac{y - 2}{1} = \frac{z}{3}$
B

$\frac{x - 3}{1} = \frac{y - 0}{1} = \frac{z - 0}{0}$
C

$\frac{x}{3} = \frac{y}{1} = \frac{z}{1}$
D

$\frac{x}{3} = \frac{y}{0} = \frac{z}{0}$

Solution

The direction cosines of any line parallel to the $x y -$ plane is $〈1, 1, 0〉$ and the coordinates of the point which are on $x -$ axis and at a distance of 3 units from the origin is $(3, 0, 0)$
Therefore, the equation of the line passing through the point $(3, 0, 0)$ and parallel to the line whose direction ratio are $〈1, 1, 0〉$ is $\frac{x - 3}{1} = \frac{y - 0}{1} = \frac{z - 0}{0}$

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