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(D) The equation of the plane is $3x + 4y + 12z - 52 = 0$. The length of the perpendicular $p$ from a point $(x_1, y_1, z_1)$ to the plane $Ax + By +

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None of these

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(D) The equation of the plane is $3x + 4y + 12z - 52 = 0$. The length of the perpendicular $p$ from a point $(x_1, y_1, z_1)$ to the plane $Ax + By + Cz + D = 0$ is given by the formula $p = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}}$. Here,the point is the origin $(0, 0, 0)$,so $x_1 = 0, y_1 = 0, z_1 = 0$. Substituting the values,we get $p = \frac{|3(0) + 4(0) + 12(0) - 52|}{\sqrt{3^2 + 4^2 + 12^2}}$. $p = \frac{|-52|}{\sqrt{9 + 16 + 144}} = \frac{52}{\sqrt{169}} = \frac{52}{13} = 4$. Since the value $4$ is not among the options $A, B, C$,the correct option is $D$.

The length of the perpendicular from the origin to the plane $3x + 4y + 12z = 52$ is

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