Textbook Question
Given vectors u and v, find: 2u.
u = 2i, v = i + j
Ch. 7 - Applications of Trigonometry and Vectors
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 8, Problem 41c
Given vectors u and v, find: v - 3u.
u = 2i, v = i + j
Verified step by step guidance1
Identify the given vectors: \( \mathbf{u} = 2\mathbf{i} \) and \( \mathbf{v} = \mathbf{i} + \mathbf{j} \).
Multiply vector \( \mathbf{u} \) by the scalar 3: calculate \( 3\mathbf{u} = 3 \times 2\mathbf{i} \).
Express \( 3\mathbf{u} \) in component form after multiplication.
Subtract \( 3\mathbf{u} \) from \( \mathbf{v} \) by subtracting corresponding components: \( \mathbf{v} - 3\mathbf{u} = (\mathbf{i} + \mathbf{j}) - (\text{components of } 3\mathbf{u}) \).
Write the resulting vector in terms of \( \mathbf{i} \) and \( \mathbf{j} \) components to complete the expression for \( \mathbf{v} - 3\mathbf{u} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Vector Representation in Component Form
Vectors can be expressed as sums of their components along the coordinate axes, typically using unit vectors i and j for the x and y directions. For example, u = 2i means the vector has a magnitude of 2 along the x-axis and zero along the y-axis.
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Position Vectors & Component Form
Scalar Multiplication of Vectors
Scalar multiplication involves multiplying each component of a vector by a scalar value. For instance, multiplying vector u by 3 scales its magnitude by 3, resulting in 3u = 6i if u = 2i.
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05:05Multiplying Vectors By Scalars
Vector Addition and Subtraction
Adding or subtracting vectors is done component-wise by combining their respective i and j components. To find v - 3u, subtract the components of 3u from those of v, resulting in a new vector.
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05:29Adding Vectors Geometrically
Related Practice
Textbook Question
Given vectors u and v, find: 2u + 3v.
u = 2i, v = i + j
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Textbook Question
Two people are carrying a box. One person exerts a force of 150 lb at an angle of 62.4° with the horizontal. The other person exerts a force of 114 lb at an angle of 54.9°. Find the weight of the box.
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Textbook Question
Given vectors u and v, find: 2u.
u = 〈-1, 2〉, v = 〈3, 0〉
Textbook Question
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