Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Vector Distance Problem
Given the vectors:
\[ \mathbf{u} = (2 + i, 0, 4 - 5i) \]
\[ \mathbf{v} = (1 + i, 2 + i, 0) \]
To find the distance between vectors \( \mathbf{u} \) and \( \mathbf{v} \):
Select one of the following options:
- \( \sqrt{47} \)
- \( \sqrt{40} \)
- \( \sqrt{45} \)
- \( \sqrt{40} \)
To solve this, you need to calculate the Euclidean distance between the two complex vectors, \(\mathbf{u}\) and \(\mathbf{v}\). The formula for the distance \( d \) between two vectors \( \mathbf{u} = (u_1, u_2, u_3) \) and \( \mathbf{v} = (v_1, v_2, v_3) \) is:
\[ d = \sqrt{(u_1 - v_1)^2 + (u_2 - v_2)^2 + (u_3 - v_3)^2} \]
First, compute the difference between corresponding components of each vector, then square each difference, sum them, and take the square root of the summation.
This exercise enhances understanding of vector distances and applying the Euclidean distance formula in a complex vector space.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffb3a58d-6965-4207-a38c-fde411a7deed%2F61dc956a-2391-47d7-ad07-faf935dce691%2Fvj8eux_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Distance Problem
Given the vectors:
\[ \mathbf{u} = (2 + i, 0, 4 - 5i) \]
\[ \mathbf{v} = (1 + i, 2 + i, 0) \]
To find the distance between vectors \( \mathbf{u} \) and \( \mathbf{v} \):
Select one of the following options:
- \( \sqrt{47} \)
- \( \sqrt{40} \)
- \( \sqrt{45} \)
- \( \sqrt{40} \)
To solve this, you need to calculate the Euclidean distance between the two complex vectors, \(\mathbf{u}\) and \(\mathbf{v}\). The formula for the distance \( d \) between two vectors \( \mathbf{u} = (u_1, u_2, u_3) \) and \( \mathbf{v} = (v_1, v_2, v_3) \) is:
\[ d = \sqrt{(u_1 - v_1)^2 + (u_2 - v_2)^2 + (u_3 - v_3)^2} \]
First, compute the difference between corresponding components of each vector, then square each difference, sum them, and take the square root of the summation.
This exercise enhances understanding of vector distances and applying the Euclidean distance formula in a complex vector space.
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