Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The length of the projected vector may be longer than the length of the vector on which it is being projected. False True

The length of the projected vector may be longer than the length of the vector on which it is being projected. False True

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
### Educational Website Content: Vector Projections **Question:** The length of the projected vector may be longer than the length of the vector on which it is being projected. - O True - O False **Explanation:** In vector mathematics, the projection of one vector onto another involves creating a new vector on the line defined by the second vector. The length of the projected vector is always less than or equal to the length of the vector that is being projected, making the statement "The length of the projected vector may be longer than the length of the vector on which it is being projected" false. **Note:** Ensure to understand the geometrical and mathematical principles behind vector projections for a more comprehensive understanding of this concept. Typically, in Euclidean geometry, the projection maintains the relationship between the lengths of the original and projected vectors according to the dot product. **Additional Resource:** For further reading, consider looking into the dot product and its relationship to vector projection. **Graph/Diagram Explanation:** No graphs or diagrams are included in this content. ### Additional Information Displayed on a device's screen at the bottom: - Temperature: 89°F - Weather: Partly sunny - Operating System: Windows 11 - Web browser: Chrome (Google Chrome icon visible) - Search bar: Active and accessible This content aims to aid students in understanding fundamental concepts in vector mathematics, particularly vector projections.
Transcribed Image Text:### Educational Website Content: Vector Projections **Question:** The length of the projected vector may be longer than the length of the vector on which it is being projected. - O True - O False **Explanation:** In vector mathematics, the projection of one vector onto another involves creating a new vector on the line defined by the second vector. The length of the projected vector is always less than or equal to the length of the vector that is being projected, making the statement "The length of the projected vector may be longer than the length of the vector on which it is being projected" false. **Note:** Ensure to understand the geometrical and mathematical principles behind vector projections for a more comprehensive understanding of this concept. Typically, in Euclidean geometry, the projection maintains the relationship between the lengths of the original and projected vectors according to the dot product. **Additional Resource:** For further reading, consider looking into the dot product and its relationship to vector projection. **Graph/Diagram Explanation:** No graphs or diagrams are included in this content. ### Additional Information Displayed on a device's screen at the bottom: - Temperature: 89°F - Weather: Partly sunny - Operating System: Windows 11 - Web browser: Chrome (Google Chrome icon visible) - Search bar: Active and accessible This content aims to aid students in understanding fundamental concepts in vector mathematics, particularly vector projections.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS