Concept explainers
To Calculate:
Distance between given point and plane.
Answer to Problem 17CLT
The perpendicular distance between the given point and the plane is
Explanation of Solution
Given Information:
Point:
Plane:
Consider the following points and plane:
Equation of the plane:
Point:
To get the perpendicular distance between then procced as follows:
Get a point on the plane by equating
Hence a point on the plane is
Now get the displacement vector between the given point and the point on the plane.
Now get the normal vector of the plane using the standard result:
Normal vector of the plane whose equation is
Hence the normal vector of the plane is
Now find the dot product of normal vector and displacement vector.
Now, get the modulus of the normal vector
Modulus of the normal vector is
Now, the value of
Therefore,
Hence, the perpendicular distance between the point and the plane is
Chapter 11 Solutions
Precalculus with Limits: A Graphing Approach
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