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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
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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