First slide

Planes in 3D

Question

$The variable plane (2 λ + 1) x + (3 - λ) y + z = 4 always passes through the line$

Moderate

A

$\frac{x}{0} = \frac{y}{0} = \frac{z - 4}{1}$
B

$\frac{x}{1} = \frac{y}{2} = \frac{z - 4}{- 3}$
C

$\frac{x}{1} = \frac{y}{1} = \frac{z - 4}{- 7}$
D

$\frac{x}{1} = \frac{y}{2} = \frac{z - 4}{- 7}$

Solution

$The plane is x + 3 y + z - 4 + λ (2 x - y) = 0$
This always passes through the line of intersection of the planes
$x + 3 y + z - 4 = 0 and 2 x - y = 0$
$Now, 2 x - y = 0 \Rightarrow \frac{x}{1} = \frac{y}{2}$
$\begin{array}{l} ∴ x + 3 y + z - 4 = 0 \\ \Rightarrow x + 3 \cdot 2 x + z - 4 = 0 \\ \Rightarrow 7 x + z - 4 = 0 \\ \Rightarrow 7 x = - (z - 4) \\ \Rightarrow \frac{x}{1} = \frac{z - 4}{- 7} \\ ∴ line is \frac{x}{1} = \frac{y}{2} = \frac{z - 4}{- 7} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App