Q. 56 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. 56 (page 631)

Find the area of the parallelogram with vertices $P_{1} = (1, 1, 1), P_{2} = (2, 3, 4), P_{3} = (6, 5, 2), a n d P_{4} = (7, 7, 5) .$

Short Answer

Expert verified

The area of the parallelogram is $18.2$ square units.

Step by step solution

Step 1. Given Information

The given vertices are $P_{1} = (1, 1, 1), P_{2} = (2, 3, 4), P_{3} = (6, 5, 2), a n d P_{4} = (7, 7, 5) .$

Step 2. Finding the area of the parallelogram

To find the area of the parallelogram we will use the formula $Area = ||u 脳 v|| .$

Let's find the two adjacent sides of a parallelogram

$u = \overset{鈫�}{P_{1} P_{2}} u = (2 - 1) i + (3 - 1) j + (4 - 1) k u = i + 2 j + 3 k v = \overset{鈫�}{P_{1} P_{3}} v = (6 - 1) i + (5 - 1) j + (2 - 1) k v = 5 i + 4 j + k$

Step 3. Solve

Let's find the cross product of the adjacent sides, the formula of the cross product is $v 脳 w = (b_{1} c_{2} - b_{2} c_{1}) i - (a_{1} c_{2} - a_{2} c_{1}) j + (a_{1} b_{2} - a_{2} b_{1}) k .$

So,

$u 脳 v = (i + 2 j + 3 k) 脳 (5 i + 4 j + k) u 脳 v = (2 路 1 - 4 路 3) i - (1 路 1 - 5 路 3) j + (1 路 4 - 5 路 2) k u 脳 v = - 10 i + 14 j - 6 k$

Now, use the formula of area of a parallelogram

$Area = ||u 脳 v|| Area = ||- 10 i + 14 j - 6 k|| Area = \sqrt{{(- 10)}^{2} + {(14)}^{2} + {(- 6)}^{2}} Area = \sqrt{332} Area 鈮� 18.2 square units$

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91影视

Find the area of the parallelogram with vertices $P_{1} = (1, 1, 1), P_{2} = (2, 3, 4), P_{3} = (6, 5, 2), a n d P_{4} = (7, 7, 5) .$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the area of the parallelogram

Step 3. Solve

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91影视

Find the area of the parallelogram with verticesP1=1,1,1,P2=2,3,4,P3=6,5,2,andP4=7,7,5.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the area of the parallelogram

Step 3. Solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the area of the parallelogram with vertices $P_{1} = (1, 1, 1), P_{2} = (2, 3, 4), P_{3} = (6, 5, 2), a n d P_{4} = (7, 7, 5) .$