Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.) 1 -4 -5 u = a v = a -2 a =
Find all values of a so that u and v are orthogonal. (Enter your answers as a comma-separated list.) 1 -4 -5 u = a v = a -2 a =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![**Orthogonality of Vectors**
Find all values of \( a \) so that **u** and **v** are orthogonal. (Enter your answers as a comma-separated list.)
\[
\mathbf{u} = \begin{bmatrix} 1 \\ -5 \\ a \\ 0 \end{bmatrix}, \quad \mathbf{v} = \begin{bmatrix} -4 \\ 1 \\ a \\ -2 \end{bmatrix}
\]
\[ a = \]
---
To solve this problem, remember that two vectors are orthogonal if their dot product is zero. Here, you can calculate the dot product of vectors **u** and **v** and then solve for \( a \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad35cd49-88f1-4759-9e4c-232c0c792d3e%2F86af5d2b-9148-499e-bff8-5e5905072306%2Fwobvw0j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Orthogonality of Vectors**
Find all values of \( a \) so that **u** and **v** are orthogonal. (Enter your answers as a comma-separated list.)
\[
\mathbf{u} = \begin{bmatrix} 1 \\ -5 \\ a \\ 0 \end{bmatrix}, \quad \mathbf{v} = \begin{bmatrix} -4 \\ 1 \\ a \\ -2 \end{bmatrix}
\]
\[ a = \]
---
To solve this problem, remember that two vectors are orthogonal if their dot product is zero. Here, you can calculate the dot product of vectors **u** and **v** and then solve for \( a \).
![Suppose that **u₁** and **u₂** are orthogonal vectors, with \( \| \mathbf{u}_1 \| = 2 \) and \( \| \mathbf{u}_2 \| = 4 \). Find \( \| 5\mathbf{u}_1 - \mathbf{u}_2 \| \).
\[ \| 5\mathbf{u}_1 - \mathbf{u}_2 \| = \underline{\hspace{2cm}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad35cd49-88f1-4759-9e4c-232c0c792d3e%2F86af5d2b-9148-499e-bff8-5e5905072306%2Fbnor3z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that **u₁** and **u₂** are orthogonal vectors, with \( \| \mathbf{u}_1 \| = 2 \) and \( \| \mathbf{u}_2 \| = 4 \). Find \( \| 5\mathbf{u}_1 - \mathbf{u}_2 \| \).
\[ \| 5\mathbf{u}_1 - \mathbf{u}_2 \| = \underline{\hspace{2cm}} \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
