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Ā = 3î + 43, B = î + 2)

Ā = 3î + 43, B = î + 2)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The vectors are defined as follows: \[ \vec{A} = 3\hat{i} + 4\hat{j}, \quad \vec{B} = \hat{i} + 2\hat{j} \] - **Vector \(\vec{A}\):** Consists of a component of 3 along the \( \hat{i} \) axis (horizontal) and 4 along the \( \hat{j} \) axis (vertical). - **Vector \(\vec{B}\):** Consists of a component of 1 along the \( \hat{i} \) axis and 2 along the \( \hat{j} \) axis. These vectors are expressed in the standard unit vector notation, where \( \hat{i} \) represents the unit vector in the horizontal direction and \( \hat{j} \) represents the unit vector in the vertical direction.
Transcribed Image Text:The vectors are defined as follows: \[ \vec{A} = 3\hat{i} + 4\hat{j}, \quad \vec{B} = \hat{i} + 2\hat{j} \] - **Vector \(\vec{A}\):** Consists of a component of 3 along the \( \hat{i} \) axis (horizontal) and 4 along the \( \hat{j} \) axis (vertical). - **Vector \(\vec{B}\):** Consists of a component of 1 along the \( \hat{i} \) axis and 2 along the \( \hat{j} \) axis. These vectors are expressed in the standard unit vector notation, where \( \hat{i} \) represents the unit vector in the horizontal direction and \( \hat{j} \) represents the unit vector in the vertical direction.
The text contains mathematical notations related to vectors: 1. **|**\(\vec{A}\)**|** - The magnitude of vector \(\vec{A}\). 2. **\(\vec{A} + \vec{B}\)** - The sum of vectors \(\vec{A}\) and \(\vec{B}\). 3. **\(\vec{A} - \vec{B}\)** - The difference between vectors \(\vec{A}\) and \(\vec{B}\). 4. **\(\vec{A} \cdot \vec{B}\)** - The dot product of vectors \(\vec{A}\) and \(\vec{B}\). 5. **\(\vec{A} \times \vec{B}\)** - The cross product of vectors \(\vec{A}\) and \(\vec{B}\). These are fundamental operations in vector algebra, used in physics and engineering to solve problems involving direction and magnitude.
Transcribed Image Text:The text contains mathematical notations related to vectors: 1. **|**\(\vec{A}\)**|** - The magnitude of vector \(\vec{A}\). 2. **\(\vec{A} + \vec{B}\)** - The sum of vectors \(\vec{A}\) and \(\vec{B}\). 3. **\(\vec{A} - \vec{B}\)** - The difference between vectors \(\vec{A}\) and \(\vec{B}\). 4. **\(\vec{A} \cdot \vec{B}\)** - The dot product of vectors \(\vec{A}\) and \(\vec{B}\). 5. **\(\vec{A} \times \vec{B}\)** - The cross product of vectors \(\vec{A}\) and \(\vec{B}\). These are fundamental operations in vector algebra, used in physics and engineering to solve problems involving direction and magnitude.
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