Consider the parallelepiped P in R³ determined by the vectors u= [2 -1 -2], v= [3 1 -2] and w = [1 -3 12]. Use the parallelogram determined by u and v as the base of P. Find the area A of the base of P. (a) A (If needed, enter √x as sqrt(x).) (b) 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. --[0 n
Consider the parallelepiped P in R³ determined by the vectors u= [2 -1 -2], v= [3 1 -2] and w = [1 -3 12]. Use the parallelogram determined by u and v as the base of P. Find the area A of the base of P. (a) A (If needed, enter √x as sqrt(x).) (b) 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. --[0 n
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter81: Introduction To Computer Numerical Control (cnc)
Section: Chapter Questions
Problem 4A: A rectangular solid has length L=12.6 mm, width W=23.8 mm, and height H=32.5 mm. Find the length of...
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![Consider the parallelepiped P in R³ determined by the vectors
u= [2 -1 -2], v= [3 1 -2] and w = [1 -3 12].
Use the parallelogram determined by u and v as the base of P.
Find the area A of the base of P.
(a)
A
(if needed, enter √x as sqrt(x).)
(b)
V=
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.
n=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0aa27a28-efdb-4d0f-aad3-266fe3536dfa%2F6e69f29f-3ccf-4f2e-94a4-65ab551d2a12%2Fv1j0x9x_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 -2] and w = [1 -3 12].
Use the parallelogram determined by u and v as the base of P.
Find the area A of the base of P.
(a)
A
(if needed, enter √x as sqrt(x).)
(b)
V=
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.
n=
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