First slide

Straight lines in 3D

Question

The equation of the line passing through $(1, - 1, 3)$ which is perpendicular to the plane $9 x - 2 y - 5 z + 4 = 0$ is

Very Easy

A

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

$\frac{x - 1}{9} = \frac{y + 1}{- 2} = \frac{z - 3}{- 5}$
C

$\frac{x - 1}{7} = \frac{y - 1}{2} = \frac{z - 1}{3}$
D

$\frac{x - 1}{9} = \frac{y + 1}{2} = \frac{z - 3}{5}$

Solution

The direction ratios of normal line to the plane $9 x - 2 y - 5 z + 4 = 0$ are $<9, - 2, - 5>$
The equation of the line passing through $(1, - 1, 3)$ which is perpendicular to the plane $9 x - 2 y - 5 z + 4 = 0$ is $\frac{x - 1}{9} = \frac{y + 1}{- 2} = \frac{z - 3}{- 5}$

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