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

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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 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.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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