First slide

Planes in 3D

Question

The nature of the intersection of the set of planes x + ay + (b + c) z + d= 0, x + by +(c + a)z + d -0 and x+ cy + (a+b)z +d=0?

Moderate

A

They meet at a point
B

They form a triangular prism
C

They pass through a line
D

They arc at equal distance from the origin

Solution

$|\begin{array}{lll} 1 a b + c \\ 1 b c + a \\ 1 c a + b \end{array}| = |\begin{array}{lll} 1 a a + b + c \\ 1 b a + b + c \\ 1 c a + b + c \end{array}| = 0$

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