Consider a parallelogram ABCD in a 3-dimensional space, where the coordinates of its vertices are A(-10,25,7), B(18,12,-30), C(5,35,13), and D(-25,15,-18). a) Find the area of the parallelogram using the dot product method. b) Determine the unit vector perpendicular to the parallelogram's plane. c) Verify your results using the cross product method. In the answer show all the detailed steps and a diagram of the parrallelogram.
Consider a parallelogram ABCD in a 3-dimensional space, where the coordinates of its vertices are A(-10,25,7), B(18,12,-30), C(5,35,13), and D(-25,15,-18). a) Find the area of the parallelogram using the dot product method. b) Determine the unit vector perpendicular to the parallelogram's plane. c) Verify your results using the cross product method. In the answer show all the detailed steps and a diagram of the parrallelogram.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 74E
Related questions
Question
Consider a parallelogram ABCD in a 3-dimensional space, where the coordinates of its vertices are A(-10,25,7), B(18,12,-30), C(5,35,13), and D(-25,15,-18).
a) Find the area of the parallelogram using the dot product method.
b) Determine the unit
c) Verify your results using the cross product method.
In the answer show all the detailed steps and a diagram of the parrallelogram.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 4 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,