First slide

Straight lines in 3D

Question

Equation of line passing through the point $(0, 0, 0)$ and parallel to a line whose direction ratios are $〈2, 3, 4〉$ is

Easy

A

$\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$
B

$\frac{x - 2}{0} = \frac{y - 3}{0} = \frac{z - 4}{3}$
C

$\frac{x - 2}{2} = \frac{y - 3}{3} = \frac{z - 4}{4}$
D

$\frac{x - 2}{0} = \frac{y - 3}{0} = \frac{z - 4}{0}$

Solution

The equation of the line passing through the point $(x_{1}, y_{1}, z_{1})$ and parallel to the line whose direction ratios are $〈a, b, c〉$ is $\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
Here the given point is $(0, 0, 0)$ and the direction ratios are $〈2, 3, 4〉$
Therefore, the equation of the required line is $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$

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