Chapter 9: Q. 20 (page 621)

Find the distance from $P_{1}$ to $P_{2}$ .
role="math" localid="1646776682625" $P_{1} = (2, - 3, - 3) a n d P_{2} = (4, 1, - 1)$

Short Answer

Expert verified

The distance between points $P_{1} = (2, - 3, - 3) a n d P_{2} = (4, 1, - 1)$ is $2 \sqrt{6}$

Step by step solution

Step 1. Given data

The given points are

$P_{1} (x_{1}, y_{1}, z_{1}) = (2, - 3, - 3) P_{2} (x_{2}, y_{2}, z_{2}) = (4, 1, - 1)$

Step 2. Distance between points

Use distance formula

$d (P_{1}, P_{2}) = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2} + {(z_{2} - z_{1})}^{2}} d (P_{1}, P_{2}) = \sqrt{{(4 - 2)}^{2} + {(1 - (- 3))}^{2} + {(- 1 - (- 3))}^{2}} d (P_{1}, P_{2}) = \sqrt{4 + 16 + 4} d (P_{1}, P_{2}) = \sqrt{24} d (P_{1}, P_{2}) = 2 \sqrt{6}$

so the distance between points is $2 \sqrt{6}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the distance from $P_{1}$ to $P_{2}$ .
role="math" localid="1646776682625" $P_{1} = (2, - 3, - 3) a n d P_{2} = (4, 1, - 1)$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Distance between points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the distance from P1toP2.role="math" localid="1646776682625" P1=(2,-3,-3)andP2=(4,1,-1)

Short Answer

Step by step solution

Step 1. Given data

Step 2. Distance between points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Pure Maths

Logic and Functions

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the distance from $P_{1}$ to $P_{2}$ .
role="math" localid="1646776682625" $P_{1} = (2, - 3, - 3) a n d P_{2} = (4, 1, - 1)$