First slide

Straight lines in 3D

Question

Equation of line parallel to the line $\frac{x - 4}{2} = \frac{y + 1}{- 3} = \frac{z + 10}{8}$ and passing through the point $(- 1, 2, 3)$ is

Easy

A

$\frac{x - 1}{2} = \frac{y - 2}{- 3} = \frac{z - 3}{8}$
B

$\frac{x + 1}{2} = \frac{y - 2}{- 3} = \frac{z - 3}{8}$
C

$\frac{x - 4}{- 1} = \frac{y + 1}{2} = \frac{z + 10}{3}$
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 $\frac{x - x_{2}}{a} = \frac{y - y_{2}}{b} = \frac{z - z_{2}}{c}$ is $\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
Here the given point is $(- 1, 2, 3)$ and the equation of the line is $\frac{x - 4}{2} = \frac{y + 1}{- 3} = \frac{z + 10}{8}$
Therefore, the equation of the required line is $\frac{x + 1}{2} = \frac{y - 2}{- 3} = \frac{z - 3}{8}$

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