1. Do you remember the scalar triple product? a. If so, then explain what it means geometrically if you have got three vectors. Illustrate with an example. b. If you need to check whether these vectors are coplanar, the scalar triple product would be zero. Suppose you were developing a game and you needed to check whether four points are coplanar, explain how you might be able to do that with scalar triple product. Explain your argument by choosing four points in the Cartesian coordinate system with three axes. c. Can you illustrate the test of coplanarity with the help of equation of a plane? Explain your argument by using the same four points you have chosen for solving the question in 1.b.
1. Do you remember the scalar triple product? a. If so, then explain what it means geometrically if you have got three vectors. Illustrate with an example. b. If you need to check whether these vectors are coplanar, the scalar triple product would be zero. Suppose you were developing a game and you needed to check whether four points are coplanar, explain how you might be able to do that with scalar triple product. Explain your argument by choosing four points in the Cartesian coordinate system with three axes. c. Can you illustrate the test of coplanarity with the help of equation of a plane? Explain your argument by using the same four points you have chosen for solving the question in 1.b.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Do you remember the scalar triple product?
a. If so, then explain what it means geometrically if you have got three vectors.
Illustrate with an example.
b. If you need to check whether these vectors are coplanar, the scalar triple product
would be zero. Suppose you were developing a game and you needed to check
whether four points are coplanar, explain how you might be able to do that with
scalar triple product. Explain your argument by choosing four points in the Cartesian
coordinate system with three axes.
c. Can you illustrate the test of coplanarity with the help of equation of a plane?
Explain your argument by using the same four points you have chosen for solving
the question in 1.b.
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