Let x, y, u and v be row vectors in R' obeying: x = (2, -1, 3), y = (-3, 2, 2), and suppose that X •W = 7, y W = -2, and u X v = (4, –2, 4). Use this information to answer the following questions: a) Calculate (x xy) x w. b) Find (x X v) · u. c) Calculate (2u – 5v) × (3u + 2v). d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectors u + kv and ku + v is 48 for some k E R. What are the possible values of k?
Let x, y, u and v be row vectors in R' obeying: x = (2, -1, 3), y = (-3, 2, 2), and suppose that X •W = 7, y W = -2, and u X v = (4, –2, 4). Use this information to answer the following questions: a) Calculate (x xy) x w. b) Find (x X v) · u. c) Calculate (2u – 5v) × (3u + 2v). d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectors u + kv and ku + v is 48 for some k E R. What are the possible values of k?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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![Let x, y, u and v be row vectors in R obeying:
х%3D (2, -1,3), у%3D (-3, 2, 2),
and suppose that
X W = 7,
y w =-2,
and uXv= (4, -2, 4).
Use this information to answer the following questions:
a) Calculate (x X y) × w.
b) Find (x X v) u.
c) Calculate (2u – 5v) × (3u + 2v).
d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectors
u + kv and ku + v is 48 for some k e R. What are the possible values of k?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9896f04-f825-497b-ab09-0c5e5b74d469%2F4746de83-bfb4-4ab2-99bd-06f45467ea72%2Fwuh2k55_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let x, y, u and v be row vectors in R obeying:
х%3D (2, -1,3), у%3D (-3, 2, 2),
and suppose that
X W = 7,
y w =-2,
and uXv= (4, -2, 4).
Use this information to answer the following questions:
a) Calculate (x X y) × w.
b) Find (x X v) u.
c) Calculate (2u – 5v) × (3u + 2v).
d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectors
u + kv and ku + v is 48 for some k e R. What are the possible values of k?
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