In the following cases, find the distance of each of the given points from the corresponding given plane.

Point Plane

(a) (0, 0, 0)

(b) (3, −2, 1)

(c) (2, 3, −5)

(d) (−6, 0, 0)

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Solution

It is known that the distance between a point, p(x₁, y₁, z₁), and a plane, Ax + By + Cz = D, is given by,

(a) The given point is (0, 0, 0) and the plane is

(b) The given point is (3, − 2, 1) and the plane is

∴

(c) The given point is (2, 3, −5) and the plane is

(d) The given point is (−6, 0, 0) and the plane is

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Similar questions

In the following exercises find the distance of each of the given points from the corresponding given plane:

$\begin{matrix} p o i n t & P l a n e (a) (0, 0, 0) & 3 x - 4 y + 12 z = 3 \end{matrix}$

$\begin{matrix} p o i n t & P l a n e (b) (3, - 2, 1) & 2 x - y + 2 z + 3 = 0 \end{matrix}$

$\begin{matrix} p o i n t & P l a n e (c) (2, 3, - 5) & x + 2 y - 2 z = 9 \end{matrix}$

$\begin{matrix} p o i n t & P l a n e (d) (- 6, 0, 0) & 2 x - 3 y + 6 z - 2 = 0 \end{matrix}$

In the following example find the distance of each of the given points from the corresponding given plane:

$\begin{matrix} p o i n t & P l a n e (2, 3, - 5) & x + 2 y - 2 z = 9 \end{matrix}$

In the following example find the distance of each of the given points from the corresponding given plane:

$\begin{matrix} p o i n t & P l a n e (3, - 2, 1) & 2 x - y + 2 z + 3 = 0 \end{matrix}$

In the following example find the distance of each of the given points from the corresponding given plane:

$\begin{matrix} p o i n t & P l a n e (- 6, 0, 0) & 2 x - 3 y + 6 z - 2 = 0 \end{matrix}$

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