First slide

Straight lines in 3D

Question

Equation of line passing through the point $(1, 0, - 3)$ and parallel to a line whose direction ratios are $〈1, 2, 2〉$ is

Moderate

A

$\frac{x - 3}{1} = \frac{y - 6}{2} = \frac{z - 2}{3}$
B

$\frac{x - 1}{1} = \frac{y - 2}{0} = \frac{z - 2}{- 3}$
C

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

$\frac{x}{1} = \frac{y}{2} = \frac{z}{2}$

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 $(1, 0, - 3)$ and the direction ratios are $〈1, 2, 2〉$
Therefore, the equation of the required line is $\frac{x - 1}{1} = \frac{y}{2} = \frac{z + 3}{2}$

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