   Chapter 12.5, Problem 72E

Chapter
Section
Textbook Problem

# Find the distance from the point to the given plane.(−6, 3, 5), x − 2y − 4z = 8

To determine

To find: The distance from the point (6,3,5) to the plane x2y4z=8.

Explanation

Formula used:

Write the expression to find the distance from the point P(x1,y1,z1) to the plane.

D=|ax1+by1+cz1+d|a2+b2+c2 (1)

Here,

x1, y1, and z1 are the coordinates of the point P(x1,y1,z1), which is (6,3,5),

a, b, and c are the normal vector numbers to the plane and

d is the constant parameter.

Write the expression to find constant parameter (d).

ax0+by0+cz0+d=0 (2)

Here,

x0, y0, and z0 are the coordinates of any point P(x0,y0,z0) in the plane.

Write the equation of the plane as follows.

x2y4z=8

Write the normal vector from the equation of the plane.

n=1,2,4

Rewrite the equation of the plane in the form of equation (2).

x2y4z8=0 (3)

Compare equations (2) and (3)

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