First slide

Planes in 3D

Question

Figure formed by the given three planes 4y + 6z = 5,2x + 3y + 5z = 5 and 6x + 5y + 9z= 0 is

Moderate

A

triangular prism
B

point
C

line
D

none of these

Solution

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

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