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Find 3u, -5v, u + v, and 5u - 4v for the given vectors u and v. (Simplify your a u = i + j, v=i- j 3u = -5v = u + v = <3,3> <-5,5> <2,0 > (3, 3) (-5,5) (2,0)

Find 3u, -5v, u + v, and 5u - 4v for the given vectors u and v. (Simplify your a u = i + j, v=i- j 3u = -5v = u + v = <3,3> <-5,5> <2,0 > (3, 3) (-5,5) (2,0)

Calculus: Early Transcendentals
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 Operations** In this exercise, we are working with two vectors, \( \mathbf{u} \) and \( \mathbf{v} \), defined as follows: - \( \mathbf{u} = \mathbf{i} + \mathbf{j} \) - \( \mathbf{v} = \mathbf{i} - \mathbf{j} \) The task is to find the following expressions and simplify them completely: 1. \( 3\mathbf{u} \) 2. \(-5\mathbf{v} \) 3. \( \mathbf{u} + \mathbf{v} \) 4. \( 5\mathbf{u} - 4\mathbf{v} \) **Solutions:** 1. **\( 3\mathbf{u} \)** - Calculation: \( 3(\mathbf{i} + \mathbf{j}) = \langle 3, 3 \rangle \) - Result: \( \langle 3, 3 \rangle \) (Correct, indicated with a check mark) 2. **\(-5\mathbf{v} \)** - Calculation: \( -5(\mathbf{i} - \mathbf{j}) = \langle -5, 5 \rangle \) - Result: \( \langle -5, 5 \rangle \) (Correct, indicated with a check mark) 3. **\( \mathbf{u} + \mathbf{v} \)** - Calculation: \( (\mathbf{i} + \mathbf{j}) + (\mathbf{i} - \mathbf{j}) = \langle 2, 0 \rangle \) - Result: \( \langle 2, 0 \rangle \) (Correct, indicated with a check mark) 4. **\( 5\mathbf{u} - 4\mathbf{v} \)** - Calculation: \( 5(\mathbf{i} + \mathbf{j}) - 4(\mathbf{i} - \mathbf{j}) = \langle 1, 9 \rangle \) - Result: \( \langle 1, 9 \rangle \) (Incorrect, indicated with a cross mark) Carefully review the calculations to find any mistakes in the final expression.
Transcribed Image Text:**Vector Operations** In this exercise, we are working with two vectors, \( \mathbf{u} \) and \( \mathbf{v} \), defined as follows: - \( \mathbf{u} = \mathbf{i} + \mathbf{j} \) - \( \mathbf{v} = \mathbf{i} - \mathbf{j} \) The task is to find the following expressions and simplify them completely: 1. \( 3\mathbf{u} \) 2. \(-5\mathbf{v} \) 3. \( \mathbf{u} + \mathbf{v} \) 4. \( 5\mathbf{u} - 4\mathbf{v} \) **Solutions:** 1. **\( 3\mathbf{u} \)** - Calculation: \( 3(\mathbf{i} + \mathbf{j}) = \langle 3, 3 \rangle \) - Result: \( \langle 3, 3 \rangle \) (Correct, indicated with a check mark) 2. **\(-5\mathbf{v} \)** - Calculation: \( -5(\mathbf{i} - \mathbf{j}) = \langle -5, 5 \rangle \) - Result: \( \langle -5, 5 \rangle \) (Correct, indicated with a check mark) 3. **\( \mathbf{u} + \mathbf{v} \)** - Calculation: \( (\mathbf{i} + \mathbf{j}) + (\mathbf{i} - \mathbf{j}) = \langle 2, 0 \rangle \) - Result: \( \langle 2, 0 \rangle \) (Correct, indicated with a check mark) 4. **\( 5\mathbf{u} - 4\mathbf{v} \)** - Calculation: \( 5(\mathbf{i} + \mathbf{j}) - 4(\mathbf{i} - \mathbf{j}) = \langle 1, 9 \rangle \) - Result: \( \langle 1, 9 \rangle \) (Incorrect, indicated with a cross mark) Carefully review the calculations to find any mistakes in the final expression.
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