Consider the parallelepiped P in R³ determined by the vectors u = [−2 −1 -2], v = [-3_1_1] and w = [1 8 -10]. 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 √√x as sqrt(x).) (b) Find the volume V of P. ν (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
Consider the parallelepiped P in R³ determined by the vectors u = [−2 −1 -2], v = [-3_1_1] and w = [1 8 -10]. 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 √√x as sqrt(x).) (b) Find the volume V of P. ν (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
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 −2], v = [−3_1 1] and w = [18–10].
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.
ν
(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%2Fd7ac4e9e-e68d-4f6c-9fda-8fdd8e8bf6e1%2F7ba30a7c-94a0-4e79-bdc4-d15c54affa74%2Fa1ar21i_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the parallelepiped P in R³ determined by the vectors
u=[−2−1 −2], v = [−3_1 1] and w = [18–10].
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.
ν
(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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