Consider the parallelepiped P in R³ determined by the vectors u= [2 -1 -1], v= [3 -1 -2] and w=[-2 2 4]. Use the parallelogram determined by u and v as the base of P. (a) A (If needed, enter √x as sqrt(x).) (b) V = Find the area A of the base of P. n Find the volume V of P. (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.
Consider the parallelepiped P in R³ determined by the vectors u= [2 -1 -1], v= [3 -1 -2] and w=[-2 2 4]. Use the parallelogram determined by u and v as the base of P. (a) A (If needed, enter √x as sqrt(x).) (b) V = Find the area A of the base of P. n Find the volume V of P. (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.
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
u= [2 -1 -1], v= [3 -1 -2] and w = [-2_2_4].
Use the parallelogram determined by u and v as the base of P.
(a)
A
(If needed, enter √x as sqrt(x).)
(b)
V =
Find the area A of the base of P.
n =
Find the volume of P.
(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0aa27a28-efdb-4d0f-aad3-266fe3536dfa%2F9953a754-253c-4bed-b8b4-c9ab59263d62%2Fafcz2dl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the parallelepiped
P in R³ determined by the vectors
u= [2 -1 -1], v= [3 -1 -2] and w = [-2_2_4].
Use the parallelogram determined by u and v as the base of P.
(a)
A
(If needed, enter √x as sqrt(x).)
(b)
V =
Find the area A of the base of P.
n =
Find the volume of P.
(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.
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