Consider the parallelepiped P in R³ determined by the vectors Use the parallelogram determined by u and v as the base of P. (a) Find the area A of the base of P. A (If needed, enter √ as sqrt(x).) (b) Find the volume V of P. v=[ u= [2 1 -1], v=[-3 1 -2] and w = [2 6 12]. (c) Find one vector n orthogonal to the base of P so that the volume of the parallelepiped determined by u, v, n equals the volume of P. n Check
Consider the parallelepiped P in R³ determined by the vectors Use the parallelogram determined by u and v as the base of P. (a) Find the area A of the base of P. A (If needed, enter √ as sqrt(x).) (b) Find the volume V of P. v=[ u= [2 1 -1], v=[-3 1 -2] and w = [2 6 12]. (c) Find one vector n orthogonal to the base of P so that the volume of the parallelepiped determined by u, v, n equals the volume of P. n Check
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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![Consider the parallelepiped P in R³ determined by the vectors
Use the parallelogram determined by u and v as the base of P.
(a) Find the area A of the base of P.
A
(If needed, enter √ as sqrt(x).)
(b) Find the volume V of P.
V=
u= [2 1 -1], v= [-3 1 -2] and w = [2 6 12].
(c) Find one vector n orthogonal to the base of P so that the volume of the parallelepiped determined by u, v, n equals the volume of P.
n=
Check](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67f82b89-727a-4a3d-8de6-b87088ff0cfe%2Fafc31832-a423-4569-96c6-2860b36cb227%2Ftmfsej_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the parallelepiped P in R³ determined by the vectors
Use the parallelogram determined by u and v as the base of P.
(a) Find the area A of the base of P.
A
(If needed, enter √ as sqrt(x).)
(b) Find the volume V of P.
V=
u= [2 1 -1], v= [-3 1 -2] and w = [2 6 12].
(c) Find one vector n orthogonal to the base of P so that the volume of the parallelepiped determined by u, v, n equals the volume of P.
n=
Check
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