For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
For each of the following pairs of vectors, find the inner-product in the specified inner-product space and determine if they are orthogonal. (a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ. (b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product. (c) sin(x) and cos(x) in the C([-π, π]) with the inner-product (f|g) 1 CπT = f(x)g(x)dx. 2πT -π •
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
Related questions
Question
Please help with parts a,b,c with solution and steps!
![For each of the following pairs of vectors, find the inner-product in the specified inner-product
space and determine if they are orthogonal.
(a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ.
(b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product.
(c) sin(x) and cos(x) in the C([-π, π]) with the inner-product
(f|g)
1
CπT
=
f(x)g(x)dx.
2πT
-π
•](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F781395ef-5933-4a4d-9640-3099b49e30d5%2F54a58774-7864-48f5-b1b9-2332867da570%2F8038itm_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the following pairs of vectors, find the inner-product in the specified inner-product
space and determine if they are orthogonal.
(a) (1,2,3) and (−1, 1, 1)† in R³ with the usual dot-product · y=xТỹ.
(b) (1,2,3) and (1,1, −2) in R³ with the usual dot-product.
(c) sin(x) and cos(x) in the C([-π, π]) with the inner-product
(f|g)
1
CπT
=
f(x)g(x)dx.
2πT
-π
•
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning