Search any question & find its solution
Question:
Answered & Verified by Expert
If the lines $a x+b y+c=0, b x+c y+a=0$ and $c x+a y+b=0$ be concurrent, then
Options:
Solution:
1978 Upvotes
Verified Answer
The correct answer is:
$a^3+b^3+c^3-3 a b c=0$
Here the given lines are
$\begin{aligned}
& a x+b y+c=0 \\
& b x+c y+a=0 \\
& c x+a y+b=0
\end{aligned}$
The lines will be concurrent, if
$\begin{aligned}
& \qquad\left|\begin{array}{lll}
a & b & c \\
b & c & a \\
c & a & b
\end{array}\right|=0 \\
& \Rightarrow a^3+b^3+c^3-3 a b c=0 .
\end{aligned}$
$\begin{aligned}
& a x+b y+c=0 \\
& b x+c y+a=0 \\
& c x+a y+b=0
\end{aligned}$
The lines will be concurrent, if
$\begin{aligned}
& \qquad\left|\begin{array}{lll}
a & b & c \\
b & c & a \\
c & a & b
\end{array}\right|=0 \\
& \Rightarrow a^3+b^3+c^3-3 a b c=0 .
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.