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3. Consider the parallelepiped P in R³ spanned by vectors u = (1,1,2), v = (1, 2, 1) and w = (2,1,1). Use the parallelogram spanned by u and v as the base of P. a) Find the area of the base of P b) Find the volume of P c) Find two vectors h and k orthogonal to the base of P so that the volume of each paral- lelepiped spanned by (u, v, h) and (u, v, k) equals the volume of P.

3. Consider the parallelepiped P in R³ spanned by vectors u = (1,1,2), v = (1, 2, 1) and w = (2,1,1). Use the parallelogram spanned by u and v as the base of P. a) Find the area of the base of P b) Find the volume of P c) Find two vectors h and k orthogonal to the base of P so that the volume of each paral- lelepiped spanned by (u, v, h) and (u, v, k) equals the volume of P.

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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3. Consider the parallelepiped P in R³ spanned by vectors u = (1,1,2), v = (1, 2, 1) and w = (2,1,1). Use the parallelogram spanned by u and v as the base of P. a) Find the area of the base of P b) Find the volume of P c) Find two vectors h and k orthogonal to the base of P so that the volume of each paral- lelepiped spanned by (u, v, h) and (u, v, k) equals the volume of P.
Transcribed Image Text:3. Consider the parallelepiped P in R³ spanned by vectors u = (1,1,2), v = (1, 2, 1) and w = (2,1,1). Use the parallelogram spanned by u and v as the base of P. a) Find the area of the base of P b) Find the volume of P c) Find two vectors h and k orthogonal to the base of P so that the volume of each paral- lelepiped spanned by (u, v, h) and (u, v, k) equals the volume of P.
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