Chapter 12: Q. 28 (page 976)

In Exercises 27–30, use the result from Example 4 to find the distance from the point P to the given plane. $P = (- 1, 3, 5), 5 x - 2 y - 7 z + 2 = 0$

Short Answer

Expert verified

$The distance from the given point to the given plane is : D = \frac{44}{\sqrt{78}} .$

Step by step solution

Step 1. Given information

$A point, P = (- 1, 3, 5); a plane, 5 x - 2 y - 7 z = - 2$

Step 2. Finding the distance from the given point to the given plane

$The distance from the point P (x_{0}, y_{0}, z_{0}) to the plane with equation a x + b y + c z = d is given by, D = \frac{| a x_{0} + b y_{0} + c z_{0} - d |}{\sqrt{a^{2} + b^{2} + c^{2}}} . Substituting the given values, we get, D = \frac{| (5) \times (- 1) + (- 2) \times (3) + (- 7) \times (5) - (- 2) |}{\sqrt{{(5)}^{2} + {(- 2)}^{2} + {(- 7)}^{2}}} \Rightarrow D = \frac{| - 5 - 6 - 35 + 2 |}{\sqrt{25 + 4 + 49}} \Rightarrow D = \frac{| - 44 |}{\sqrt{78}} \Rightarrow D = \frac{44}{\sqrt{78}}$

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In Exercises 27–30, use the result from Example 4 to find the distance from the point P to the given plane. $P = (- 1, 3, 5), 5 x - 2 y - 7 z + 2 = 0$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the distance from the given point to the given plane

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In Exercises 27–30, use the result from Example 4 to find the distance from the point P to the given plane.P=(−1,3,5),5x−2y−7z+2=0

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the distance from the given point to the given plane

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Statistics

Geometry

Study anywhere. Anytime. Across all devices.

In Exercises 27–30, use the result from Example 4 to find the distance from the point P to the given plane. $P = (- 1, 3, 5), 5 x - 2 y - 7 z + 2 = 0$