First slide

Straight lines in 3D

Question

Equation of line passing through the point $(0, 0, 0)$ and equally inclined to the coordinate axes is

Very Easy

A

$x = y = z$
B

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

$\frac{x - 1}{3} = \frac{y - 0}{6} = \frac{z - 3}{2}$
D

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

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 $⟨ 1, 1, 1 ⟩$ because this line makes equal angles with axes.
Therefore, the equation of the required line is $x = y = z$

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