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The points (0,0,0) and (2,5,7) lie on the same side of the plane $2 x + a y + 3 z + 1 = 0$ if

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$a > 0$

$a < \frac{- 26}{5}$

$a > \frac{- 26}{5}$

$a < 0$

answer is D.

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Detailed Solution

$A = (0, 0, 0), B = (2, 5, 7)$

A,B lies same side

i.e. $\frac{- L_{11}}{L_{22}} < 0$

$\frac{- 1}{4 + 5 a + 21 + 1} < 0$

$5 a + 26 > 0$

$5 a > - 26$

$a > \frac{- 26}{5}$

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