Let ū = (3,1), v = (-8,4), and w = (-6, -2). Calculate the value of each expression. d) |ū+ v e) |ū| + |w|

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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**Vectors and Operations**

Let \(\mathbf{u} = \langle 3, 1 \rangle\), \(\mathbf{v} = \langle -8, 4 \rangle\), and \(\mathbf{w} = \langle -6, -2 \rangle\). Calculate the value of each expression:

a) \(\mathbf{u} - \mathbf{v}\)

b) \(\mathbf{v} + \mathbf{w}\)

c) \(\mathbf{u} - \mathbf{w}\)

d) \(|\mathbf{u} + \mathbf{v}|\)

e) \(|\mathbf{u} + \mathbf{w}|\)

f) Draw the resultant and find algebraically: \(2\mathbf{u} + \mathbf{v} + \mathbf{w}\)

**Graph Explanation:**

The grid provided is a standard Cartesian plane with the x-axis and y-axis ranging from -10 to 10. It is used to draw and visualize vector operations to better understand resultant vectors and their components.
Transcribed Image Text:**Vectors and Operations** Let \(\mathbf{u} = \langle 3, 1 \rangle\), \(\mathbf{v} = \langle -8, 4 \rangle\), and \(\mathbf{w} = \langle -6, -2 \rangle\). Calculate the value of each expression: a) \(\mathbf{u} - \mathbf{v}\) b) \(\mathbf{v} + \mathbf{w}\) c) \(\mathbf{u} - \mathbf{w}\) d) \(|\mathbf{u} + \mathbf{v}|\) e) \(|\mathbf{u} + \mathbf{w}|\) f) Draw the resultant and find algebraically: \(2\mathbf{u} + \mathbf{v} + \mathbf{w}\) **Graph Explanation:** The grid provided is a standard Cartesian plane with the x-axis and y-axis ranging from -10 to 10. It is used to draw and visualize vector operations to better understand resultant vectors and their components.
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