First slide

Straight lines in 3D

Question

The equation of a line which is perpendicular to the plane $5 x + 2 y - 8 z = 0$ and passing through $(- 1, 0, 1)$ is

Moderate

A

$\frac{x + 1}{5} = \frac{y}{2} = \frac{z - 1}{- 8}$
B

$\frac{x - 1}{5} = \frac{y - 1}{0} = \frac{z - 1}{- 8}$
C

$\frac{x + 1}{8} = \frac{z - 1}{2} = \frac{y - 0}{2}$
D

$\frac{x - 5}{- 1} = \frac{y - 2}{0} = \frac{z + 2}{1}$

Solution

The equation of a line passing through the point $(x_{1}, y_{1}, z_{1})$ and perpendicular to the plane $a x + b y + c z + d = 0$ is $\frac{x - x_{1}}{a} = \frac{y - y_{1}}{b} = \frac{z - z_{1}}{c}$
Therefore, the equation of a line which is perpendicular to the plane $5 x + 2 y - 8 z = 0$ and passing through $(- 1, 0, 1)$ is $\frac{x + 1}{5} = \frac{y}{2} = \frac{z - 1}{- 8}$

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