Find the distance of the point (0, 0, 0) from | vedclass

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(A) The distance $d$ of a point $P(x_1, y_1, z_1)$ from a plane $Ax + By + Cz - D = 0$ is given by the formula:$d = \left| \frac{Ax_1 + By_1 + Cz_1 -

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$3$

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(A) The distance $d$ of a point $P(x_1, y_1, z_1)$ from a plane $Ax + By + Cz - D = 0$ is given by the formula:$d = \left| \frac{Ax_1 + By_1 + Cz_1 - D}{\sqrt{A^2 + B^2 + C^2}} \right|$Given the point $(x_1, y_1, z_1) = (0, 0, 0)$ and the plane equation $3x - 4y + 12z - 3 = 0$,we identify $A = 3, B = -4, C = 12$,and $D = 3$.Substituting these values into the formula:$d = \left| \frac{3(0) - 4(0) + 12(0) - 3}{\sqrt{3^2 + (-4)^2 + 12^2}} \right|$$d = \left| \frac{-3}{\sqrt{9 + 16 + 144}} \right|$$d = \left| \frac{-3}{\sqrt{169}} \right|$$d = \frac{3}{13}$

Find the distance of the point $(0, 0, 0)$ from the plane $3x - 4y + 12z = 3$. (in $/13$)

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