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Consider the parallelepiped P in R' determined by the vectors u = [0 -1 2], v = [-1 1 -1] and w = [-1 -2 -2]. Use the parallelogram determined by u and v as the base of P. (a) (2 marks) Find the area A of the base of P. A sqrt(6) (If needed, enter Va as sqrt(æ).) (b) (1 mark) Find the volume V of P. V = 7 (C) (2 marks) Find one vector n orthogonal to the base of P that the volume of the parallelepiped determined by u, v, n equals the volume of P. n =

Consider the parallelepiped P in R' determined by the vectors u = [0 -1 2], v = [-1 1 -1] and w = [-1 -2 -2]. Use the parallelogram determined by u and v as the base of P. (a) (2 marks) Find the area A of the base of P. A sqrt(6) (If needed, enter Va as sqrt(æ).) (b) (1 mark) Find the volume V of P. V = 7 (C) (2 marks) Find one vector n orthogonal to the base of P that the volume of the parallelepiped determined by u, v, n equals the volume of P. n =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section: Chapter Questions
Problem 4DE
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Consider the parallelepiped P in R° determined by the vectors u = [0 -1 2], v = [-1 1 -1] and w = [-1 -2 -2]. Use the parallelogram determined by u and v as the base of P. (a) (2 marks) Find the area A of the base of P. A = sqrt(6) (If needed, enter Va as sqrt(æ).) (b) (1 mark) Find the volume V of P. V = 7 (c) (2 marks) 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 =
Transcribed Image Text:Consider the parallelepiped P in R° determined by the vectors u = [0 -1 2], v = [-1 1 -1] and w = [-1 -2 -2]. Use the parallelogram determined by u and v as the base of P. (a) (2 marks) Find the area A of the base of P. A = sqrt(6) (If needed, enter Va as sqrt(æ).) (b) (1 mark) Find the volume V of P. V = 7 (c) (2 marks) 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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