Question:
Consider the following system of equations :
$x+2 y-3 z=a$
$2 x+6 y-11 z=b$
$x-2 y+7 z=c$
where $a, b$ and $c$ are real constants. Then the system of equations :
Correct Option: , 2
Solution:
$P_{1}: x+2 y-3 z=a$
$P_{2}: 2 x+6 y-11 z=b$
$P_{3}: x-2 y+7 z=c$
Clearly
$5 P_{1}=2 P_{2}+P_{3} \quad$ if $5 a=2 b+c$
$\Rightarrow$ All the planes sharing a line of intersection
$\Rightarrow$ infinite solutions