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Combination

The three str...

Question

The three straight lines $a x + b y = c, b x + c y = a$ and $c x + a y = b$ are collinear, if.

b + c = a

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c + a = b

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a + b + c = 0

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a + b = c

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Solution

The correct option is C $a + b + c = 0$
Given lines are
$a x + b y = c,$
$b x + c y = a,$
$c x + a y = b$
On adding these three lines, we get
$a x + b y + b x + c y + c x + a y = a + b + c$
$\Rightarrow (a + b + c) x + (a + b + c) y = a + b + c$
For collinearity, $0 x + 0 y = 0$
On comparing, we get
$a + b + c = 0$

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