Assertion :Lines $3 x + 4 y + 6 = 0. \sqrt{2} x + \sqrt{3} y + 2 \sqrt{2} = 0$ and $4 x + 7 y + 8 = 0$ are concurrent. Reason: If three lines are concurrent then determinant of coefficients should be non-zero.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
$∣ ∣ ∣ ∣ ∣ \begin{matrix} 3 & 4 & 6 \sqrt{2} & \sqrt{3} & 2 \sqrt{2} 4 & 7 & 8 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$= 3 (8 \sqrt{3} - 14 \sqrt{2}) - 4 (8 \sqrt{2} - 8 \sqrt{2}) + 6 (7 \sqrt{2} - 4 \sqrt{3})$
$\Rightarrow 24 \sqrt{3} - 42 \sqrt{2} + 42 \sqrt{2} - 24 \sqrt{3} = 0$
Lines are concurrent
(C) Assertion is correct; Reason is incorrect.

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Assertion :Lines 3x+4y+6=0.√2x+√3y+2√2=0 and 4x+7y+8=0 are concurrent. Reason: If three lines are concurrent then determinant of coefficients should be non-zero.

The correct option is C Assertion is correct but Reason is incorrect∣∣ ∣ ∣∣346√2√32√2478∣∣ ∣ ∣∣=3(8√3−14√2)−4(8√2−8√2)+6(7√2−4√3)⇒24√3−42√2+42√2−24√3=0Lines are concurrent(C) Assertion is correct; Reason is incorrect.

Assertion :Lines $3 x + 4 y + 6 = 0. \sqrt{2} x + \sqrt{3} y + 2 \sqrt{2} = 0$ and $4 x + 7 y + 8 = 0$ are concurrent. Reason: If three lines are concurrent then determinant of coefficients should be non-zero.