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
icon
Related questions
Question
Plz correct solution.
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.
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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps with 43 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,