First slide

Straight lines in 3D

Question

The symmetric form of the line passing through a point $(1, 0, 3)$ and having direction ratios $⟨ 1, 0, 3 ⟩$ is

Easy

A

$x - 1 = y = 3 (z - 3)$
B

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

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

$x - 1 = y = - 3 (z - 3)$

Solution

The equation of a line which is passing through the point $(x_{1}, y_{1}, z_{1})$ and having direction ratios $⟨ a, b, c ⟩$ is $\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
Therefore, the equation of a line which is passing through the point $(1, 0, 3)$ and having direction ratios $⟨ 1, 0, 3 ⟩$ is $\frac{x - 1}{1} = \frac{y}{0} = \frac{z - 3}{3}$

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