Straight Lines and Pair of Straight Lines PYQ — JEE Advanced 2007 · Shift 1 · Q42 with Solution

Consider the following linear equations

$ax + by + cz = 0$

$bx + cy + az = 0$

$cx + ay + bz = 0$

Match the conditions/expressions in Column I with statements in Column II.

	Column I		Column II
(A)	$a + b + c e 0$ and ${a^2} + {b^2} + {c^2} = ab + bc + ca$	(P)	the equations represent planes meeting only at a single point.
(B)	$a + b + c = 0$ and ${a^2} + {b^2} + {c^2} e ab + bc + ca$	(Q)	the equations represent the line $x=y=z$ .
(C)	$a + b + c e 0$ and ${a^2} + {b^2} + {c^2} e ab + bc + ca$	(R)	the equations represent identical planes.
(D)	$a + b + c = 0$ and ${a^2} + {b^2} + {c^2} = ab + bc + ca$	(S)	the equations represent the whole of the three dimensional space.

Straight Lines and Pair of Straight Lines question