First slide

Planes in 3D

Question

$The three planes 4 y + 6 z = 5, 2 x + 3 y + 5 z = 5 and 6 x + 5 y + 9 z = 10$

Moderate

A

meet in a point
B

have a line in common
C

form a triangular prism
D

none of these

Solution

Plane passing through the line of intersection of planes
$\begin{array}{l} 4 y + 6 z = 5 and 2 x + 3 y + 5 z = 5 is \\ (4 y + 6 z - 5) + λ (2 x + 3 y + 5 z - 5) = 0 \\ or 2 λ x + (3 λ + 4) y + (5 λ + 6) z - 5 λ - 5 = 0 \end{array}$
$Clearly, for λ = - 3, we get the plane 6 x + 5 y + 9 z = 10$
$Hence, the given three planes have common line of intersection.$

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