If the equation of the plane $2 x - 3 y + 6 z = 7$ in the normal from is $l x + m y + n z = P$ then $l + P =$

9

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\frac{9}{49}

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\frac{9}{7}

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\frac{51}{7}

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Solution

The correct option is C $\frac{9}{7}$
Plane $: 2 x - 3 y + 67 = 7$
normal form $\to r .^n = p$ where $^n$ is unit normal vector.
$∴$ In normal form,
$\frac{2 x - 3 y + 6 z}{\sqrt{2^{2} + 3^{2} + 6^{2}}} = \frac{7}{\sqrt{2^{2} + 3^{2} + 6^{2}}} \frac{2 x - 3 y + 6 z}{7} = \frac{7}{7} - (i)$
Comparing $(i)$ with $l x + m y + n z = p$
$l = \frac{2}{7}, p = 1 ∴ l + p = \frac{9}{7}$

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