Example 1: Find the length of the following vectors. (a) = (4, 3) (b) u = (1, 1, 3, 0)
Example 1: Find the length of the following vectors. (a) = (4, 3) (b) u = (1, 1, 3, 0)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Example 1: Find the length of the following vectors.
**(a)** \(\vec{v} = (4, 3)\)
**(b)** \(\vec{u} = (1, 1, 3, 0)\)
---
To calculate the length (or magnitude) of a vector, use the formula for a 2-dimensional or n-dimensional vector:
- For a 2-dimensional vector \(\vec{v} = (x, y)\), the length \(|\vec{v}|\) is calculated as:
\[
|\vec{v}| = \sqrt{x^2 + y^2}
\]
- For an n-dimensional vector \(\vec{u} = (x_1, x_2, \ldots, x_n)\), the length \(|\vec{u}|\) is calculated as:
\[
|\vec{u}| = \sqrt{x_1^2 + x_2^2 + \ldots + x_n^2}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57fbb07-e1bd-418f-9d01-1252f5b1cb71%2Fddd6da27-0aab-452c-8e6f-fa5c1338af66%2Fvgrn28a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example 1: Find the length of the following vectors.
**(a)** \(\vec{v} = (4, 3)\)
**(b)** \(\vec{u} = (1, 1, 3, 0)\)
---
To calculate the length (or magnitude) of a vector, use the formula for a 2-dimensional or n-dimensional vector:
- For a 2-dimensional vector \(\vec{v} = (x, y)\), the length \(|\vec{v}|\) is calculated as:
\[
|\vec{v}| = \sqrt{x^2 + y^2}
\]
- For an n-dimensional vector \(\vec{u} = (x_1, x_2, \ldots, x_n)\), the length \(|\vec{u}|\) is calculated as:
\[
|\vec{u}| = \sqrt{x_1^2 + x_2^2 + \ldots + x_n^2}
\]
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