Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Vector Magnitude Calculations
Given the vectors:
\[ \mathbf{u} = \left\langle 1, \frac{1}{2} \right\rangle \]
\[ \mathbf{v} = \left\langle 5, 8 \right\rangle \]
Find the following:
#### (a) Magnitude of \(\mathbf{u}\)
\[ \|\mathbf{u}\| \]
\[ \underline{\hspace{8cm}} \]
#### (b) Magnitude of \(\mathbf{v}\)
\[ \|\mathbf{v}\| \]
\[ \underline{\hspace{8cm}} \]
#### (c) Magnitude of the sum of \(\mathbf{u}\) and \(\mathbf{v}\)
\[ \|\mathbf{u} + \mathbf{v}\| \]
\[ \underline{\hspace{8cm}} \]
#### (d) Magnitude of \(\mathbf{u}\) over the magnitude of \(\mathbf{u}\)
\[ \left\| \frac{\mathbf{u}}{\|\mathbf{u}\|} \right\| \]
\[ \underline{\hspace{8cm}} \]
#### (e) Magnitude of \(\mathbf{v}\) over the magnitude of \(\mathbf{v}\)
\[ \left\| \frac{\mathbf{v}}{\|\mathbf{v}\|} \right\| \]
\[ \underline{\hspace{8cm}} \]
#### (f) Magnitude of the sum of \(\mathbf{u}\) and \(\mathbf{v}\) over the magnitude of the sum of \(\mathbf{u}\) and \(\mathbf{v}\)
\[ \left\| \frac{\mathbf{u} + \mathbf{v}}{\|\mathbf{u} + \mathbf{v}\|} \right\| \]
\[ \underline{\hspace{8cm}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63d16113-ff39-4f92-89f8-61ce82bfb495%2Fd4307818-4692-41d9-a2e1-165756ea005a%2Ftihmtoo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Vector Magnitude Calculations
Given the vectors:
\[ \mathbf{u} = \left\langle 1, \frac{1}{2} \right\rangle \]
\[ \mathbf{v} = \left\langle 5, 8 \right\rangle \]
Find the following:
#### (a) Magnitude of \(\mathbf{u}\)
\[ \|\mathbf{u}\| \]
\[ \underline{\hspace{8cm}} \]
#### (b) Magnitude of \(\mathbf{v}\)
\[ \|\mathbf{v}\| \]
\[ \underline{\hspace{8cm}} \]
#### (c) Magnitude of the sum of \(\mathbf{u}\) and \(\mathbf{v}\)
\[ \|\mathbf{u} + \mathbf{v}\| \]
\[ \underline{\hspace{8cm}} \]
#### (d) Magnitude of \(\mathbf{u}\) over the magnitude of \(\mathbf{u}\)
\[ \left\| \frac{\mathbf{u}}{\|\mathbf{u}\|} \right\| \]
\[ \underline{\hspace{8cm}} \]
#### (e) Magnitude of \(\mathbf{v}\) over the magnitude of \(\mathbf{v}\)
\[ \left\| \frac{\mathbf{v}}{\|\mathbf{v}\|} \right\| \]
\[ \underline{\hspace{8cm}} \]
#### (f) Magnitude of the sum of \(\mathbf{u}\) and \(\mathbf{v}\) over the magnitude of the sum of \(\mathbf{u}\) and \(\mathbf{v}\)
\[ \left\| \frac{\mathbf{u} + \mathbf{v}}{\|\mathbf{u} + \mathbf{v}\|} \right\| \]
\[ \underline{\hspace{8cm}} \]
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