Answered: -) Are these pairs of vectors… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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Question

(1) Are these pairs of vectors orthonormal or only orthogonal or only linearly independent?
[7]; « []
1
and
0.4
sin 0
-1
0.6
Cos O
|
(a)
and
(c)
and
Cos O
Change the second vector when necessary to produce orthonormal vectors.
1
0.8
–0.3
sin 0

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Are these pairs of vectors orthonormal or only orthogonal or only independent? (a) (b) .6 .8 Cos sin 0 .3 (c) and sin COS Change the second vector when necessary to produce orthonormal vectors.
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3 = [ ¹₂ ], b = [ ³ ], c = [ ¹₁ ], d = [¯^¹'], and v = [¯2²], 5. Given vectors a = (a) Find all real numbers x₁, x2, x3, x4, such that x₁a + x₂b + x3c + x4d = v (b) Write [at least] one sentence about what you have done above using the following mathematical term: linear combination. (c) Write [at least] one sentence about what you have done above using the following mathematical term: span.
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"I Suppose that u and v are vectors in R' and c is a scalar. Decide whether each statement is always true or not always true. Be sure you can explain why your answers are correct! Always true 1. (cũ) - ở = ủ - (cỡ) = c(u . 7) Not always true v 2. (i x ở) - ũ = ở· (ũ x ở) Always true 3. (cũ) x ở = i x (cỡ) = c(u × 7) Not always true v 4. (i x ũ) - ũ = 0
Find the values of the constants that make the set of vectors orthonormal.
The dot product of two vectors X1 Yi X2 y2 and y = X = Xn Yn in R" is defined by x· y = x1yı + x2Y2 + perpendicular if x· y = 0. Any vector in R' perpendicular to X • + xnYn. The vectors x and y are called ... 3 6. can be written in the form s+ t.
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