If $a$ and $b$ are two non collinear vectors then the points $l_{1} a + m_{1} b, l_{2} a + m_{2} b, l_{3} a + m_{3} b$ are collinear if

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$\sum l_{1} (m_{2} + m_{3}) = 0$

$\sum l_{1} (m_{2} - m_{3}) = 0$

$\sum l_{3} (m_{2} - m_{3}) = 0$

answer is B.

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Detailed Solution

$Ab = (l_{2} - l_{1}) a + (m_{2} - m_{1}) b Ac = (l_{3} - l_{1}) a + (m_{3} - m_{1}) b AB, AC are collinear \Rightarrow \frac{l_{2} - l_{1}}{l_{3} - l_{1}} = \frac{m_{2} - m_{1}}{m_{3} - m_{1}}$

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