To Prove: that the volume V of a parallelepiped with
Explanation of Solution
Given information:
A parallelepiped with vector u, v and w as adjacent edges.
Concept used:
A polyhedron whose all faces are parallelogram is called parallelepiped.
The volume of the parallelepiped will be the product of its height and area of its base.
The area of base will be the cross product of the base vector.
Calculation:
This figure shows a parallelepiped with u, v and w as adjacent edges.
Let
Here area of base will be the cross product of the base vector that is
Height of the parallelepiped is the projection of vector u on
Also
Hence
Therefore the volume of a parallelepiped is
Conclusion:
The volume of a parallelepiped with vector u, v and w as adjacent edges is
Chapter 11 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning