Q. What is the nature of the intersection of the set of planes $x + ay + (b + c)\mathcal{z} + d = 0,\ x + by + (c + a)\mathcal{z} + d = 0$ and $x + cy + (a + b)\mathcal{z} + d = 0$?
A) They meet at a point
B) They form a triangular prism
C) They pass through a line
D) They are at equal distance from the origin
Explanation
(c)
$\left| \begin{matrix}
1 & a & b + c \\
1 & b & c + a \\
1 & c & a + b
\end{matrix} \right| = \left| \begin{matrix}
1 & a & a + b + c \\
1 & b & a + b + c \\
1 & c & a + b + c
\end{matrix} \right| = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.