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Calculating Area/Volume using determinants. An interesting application of determinants is that it can be used to calculate the area/volume of particular geometric objects. It can be shown that • In three-dimensional space, the volume of the parallelepiped box spanned by the vectors u = -8-- and w= h is given as ad g e h fl Volume = absolute value of b C 2. What is the volume of the parallelepiped determined by the vectors u = 8---1 1. v= Now w a d -0---0 b V = e C 32 --0₂ 3 ? and w=

Calculating Area/Volume using determinants. An interesting application of determinants is that it can be used to calculate the area/volume of particular geometric objects. It can be shown that • In three-dimensional space, the volume of the parallelepiped box spanned by the vectors u = -8-- and w= h is given as ad g e h fl Volume = absolute value of b C 2. What is the volume of the parallelepiped determined by the vectors u = 8---1 1. v= Now w a d -0---0 b V = e C 32 --0₂ 3 ? and w=

Advanced Engineering Mathematics
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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Calculating Area/Volume using determinants. An interesting application of determinants is that it can be used to calculate the area/volume of particular geometric objects. It can be shown that • In three-dimensional space, the volume of the parallelepiped box spanned by the vectors u = 9 1₁ h and w= is given as a Volume = absolute value of b с d 9 e h 2. What is the volume of the parallelepiped determined by the vectors u = 4 3 0₁-0 2 a 8-₁-4 b v= , v = 3 and w= 3 ?
Transcribed Image Text:Calculating Area/Volume using determinants. An interesting application of determinants is that it can be used to calculate the area/volume of particular geometric objects. It can be shown that • In three-dimensional space, the volume of the parallelepiped box spanned by the vectors u = 9 1₁ h and w= is given as a Volume = absolute value of b с d 9 e h 2. What is the volume of the parallelepiped determined by the vectors u = 4 3 0₁-0 2 a 8-₁-4 b v= , v = 3 and w= 3 ?
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