Q. 52 find the area of the parallelogr... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 52 (page 627)

find the area of the parallelogram with vertices P1 , P2 , P3 , and P4 .
$P_{1} = (2, 1, 1) P_{2} = (2, 3, 1) P_{3} = (- 2, 4, 1) P_{4} = (- 2, 6, 1)$

Short Answer

Expert verified

$A r e a = 5 s q u n i t s$

Step by step solution

Step 1. Area of parallelogram

We know that area of parallelogram is given as :

$\overset{鈫�}{u} 脳 \overset{鈫�}{v}$

where ;

u and v being the vector of adjacent sides of parallelogram

Step 2. Solving for vectors u→ & v→

$\overset{鈫�}{u} = P_{1} P_{2} \overset{鈫�}{u} = (2, 3, 1) - (2, 1, 1) \overset{鈫�}{u} = (0, 2, 0) \overset{鈫�}{v} = \overset{鈫�}{P_{1} P_{4}} \overset{鈫�}{v} = (- 2, 4, 1) - (2, 1, 1) \overset{鈫�}{v} = (- 4, 3, 0)$

We can write these vectors as:

$\overset{鈫�}{u} = 0 \hat{i} + 2 \hat{j} + 0 \hat{k} \overset{鈫�}{v} = - 4 \hat{i} + 3 \hat{j} + 0 \hat{k}$

Step 3. Area is equals to

$A r e a = | \overset{鈫�}{u} 脳 \overset{鈫�}{v} | \overset{鈫�}{u} 脳 \overset{鈫�}{v} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 2 & 0 \\ - 4 & 3 & 0 \end{matrix}| \overset{鈫�}{u} 脳 \overset{鈫�}{v} = \hat{i} (0) - \hat{j} (0) + \hat{k} (8) \overset{鈫�}{u} 脳 \overset{鈫�}{v} = 8 \hat{k} 鈬� A r e a = | \overset{鈫�}{u} 脳 \overset{鈫�}{v} | = 8 s q u n i t s$

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91影视

find the area of the parallelogram with vertices P1 , P2 , P3 , and P4 .
$P_{1} = (2, 1, 1) P_{2} = (2, 3, 1) P_{3} = (- 2, 4, 1) P_{4} = (- 2, 6, 1)$

Short Answer

Step by step solution

Step 1. Area of parallelogram

Step 2. Solving for vectors u→ & v→

Step 3. Area is equals to

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91影视

find the area of the parallelogram with vertices P1 , P2 , P3 , and P4 .P1=(2,1,1)P2=(2,3,1)P3=(-2,4,1)P4=(-2,6,1)

Short Answer

Step by step solution

Step 1. Area of parallelogram

Step 2. Solving for vectors u→ & v→

Step 3. Area is equals to

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Mechanics Maths

Logic and Functions

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

find the area of the parallelogram with vertices P1 , P2 , P3 , and P4 .
$P_{1} = (2, 1, 1) P_{2} = (2, 3, 1) P_{3} = (- 2, 4, 1) P_{4} = (- 2, 6, 1)$