First slide

Straight lines in 3D

Question

The equation of the plane which passes through the z-axis and is perpendIcular to the line $\frac{x - a}{\cos θ} = \frac{y + 2}{\sin θ} = \frac{z - 3}{0}$ is

Moderate

A

$x + y \tan θ = 0$
B

$y + x \tan θ = 0$
C

$x \cos θ - y \sin θ = 0$
D

$x \sin θ - y \cos θ = 0$

Solution

The d.r’s of the normal of the plane are ( $\cos θ, \sin θ$ , 0).
Now, the required plane passes through the z-axis. hence the point (0,0,0) lies on the plane.
The required plane is $x \cos θ + y \sin θ = 0$ , $\Rightarrow x + y \tan θ = 0$

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