First slide

Straight lines in 3D

Question

The equation of a line passing through the point on $z -$ axis at a distance of 1 unit from the origin and having direction ratios $〈1, 0, - 1〉$ is

Easy

A

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

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

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

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

Solution

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

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