First slide

Straight lines in 3D

Question

Equation of a line passing through $(- 1, 2, - 3)$ and perpendicular to the plane $2 x + 3 y + z + 5 = 0$ is

Very Easy

A

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

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

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

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

Solution

The direction ratios of normal to the plane $2 x + 3 y + z + 5 = 0$ are $⟨ 2, 3, 1 ⟩$
Hence the equation of the line passing through the point $(- 1, 2, - 3)$ and having direction ratios $⟨ 2, 3, 1 ⟩$ is $\frac{x + 1}{2} = \frac{y - 2}{3} = \frac{z + 3}{1}$

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