Let x, y, u and v be row vectors in R' obeying: х%3 (2, -1,3), у%3D(-3, 2, 2), and suppose that X •w = 7, y w = -2, and ux v = (4, –2, 4). Use this information to answer the following questions: a) Calculate (x X y) x w. b) Find (x x v) u. c) Calculate (2u - 5v) x (3u + 2v). d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectorsu+ kv and ku + v is 48 for some k ER.What are the possible values of k?
Let x, y, u and v be row vectors in R' obeying: х%3 (2, -1,3), у%3D(-3, 2, 2), and suppose that X •w = 7, y w = -2, and ux v = (4, –2, 4). Use this information to answer the following questions: a) Calculate (x X y) x w. b) Find (x x v) u. c) Calculate (2u - 5v) x (3u + 2v). d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectorsu+ kv and ku + v is 48 for some k ER.What are the possible values of k?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hi there, I am struggling to answer part d), I was wondering if you could help. I attached a picture of my answers to parts a), b) and c). Thank you!
Transcribed Image Text:3D19(4,-2,4)
ー4(4,-2,4)+15(4ュ-2,4)
(76,-38, 76)
ニ
(^x^)Oエ-(Mx ^) S-
11
= -8-2-12
(x xV).u%3D-22
-ユ7,1スッ20)
=子(-3,2,2)+ス(2,-1,3) (xxV)-u=x·(-4,2,-4)
ニ子ィー(-スx)
=(2,-1,3).(4,2スュー分)
(カーとカフ=m×>
(-21,14,14) +(4,-2.
ニ
>ワー:
(M x ^).X= · (^x x) (9
(X४-) -
x (M .h)-h(m-x)=
mxchxx) (0
<xu = -(4-ス,4)
||
ニ
(4 4)×m とー=M·h
モ=M·X
X.W=7 4-w =-2 uxv = (4,-2,4)
ニX
Transcribed Image Text:3
Let x, y, u and v be row vectors in R obeying:
X =
x = (2, –1, 3), y = (-3, 2, 2),
and suppose that
X•w = 7, y w = -2,
and ux v = (4, -2, 4).
Use this information to answer the following questions:
a) Calculate (x X y) X w.
b) Find (x X v) ·u.
c) Calculate (2u - 5v) x (3u + 2v).
d) Suppose that the area of the parallelogram with one vertex at the origin determined by the vectorsu + kv
and ku + v is 48 for some k E R. What are the possible values of k?
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