If the lines (b x + c y + a = 0) and (c x + a y + b = 0) be... | MATH - SLOPE OF LINE, EQUATION OF LINE IN | SolveeIt

If the lines $b x + c y + a = 0$ and

$c x + a y + b = 0$ be concurrent, then

$a ^ { 3 } + b ^ { 3 } + c ^ { 3 } + 3 a b c = 0$

$a ^ { 3 } + b ^ { 3 } + c ^ { 3 } - a b c = 0$

$a ^ { 3 } + b ^ { 3 } + c ^ { 3 } - 3 a b c = 0$

None of these

Answer

$a ^ { 3 } + b ^ { 3 } + c ^ { 3 } - 3 a b c = 0$

Explanation

Here the given lines are, $b x + c y + a = 0$ ,

$c x + a y + b = 0$

The lines will be concurrent, iff $\left| \begin{array} { l l l } a & b & c \\ b & c & a \\ c & a & b \end{array} \right| = 0$

⇒ $a ^ { 3 } + b ^ { 3 } + c ^ { 3 } - 3 a b c = 0$

Question: If the lines \(b x + c y + a = 0\) and \(c x + a y + b = 0\) be concurrent, then...