Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
8. Vectors
Geometric Vectors
Problem 7.34a
Textbook Question
Textbook QuestionGiven u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.
v - u
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Vector Subtraction
Vector subtraction involves finding the difference between two vectors by subtracting their corresponding components. For vectors u = 〈u1, u2〉 and v = 〈v1, v2〉, the result of v - u is given by 〈v1 - u1, v2 - u2〉. This operation is fundamental in vector analysis and is used to determine the relative position of one vector to another.
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Component Form of Vectors
Vectors can be expressed in component form, which represents them as ordered pairs or triples. In this case, u = 〈-2, 5〉 and v = 〈4, 3〉 are two-dimensional vectors where the first component indicates the horizontal direction and the second component indicates the vertical direction. Understanding component form is essential for performing operations like addition and subtraction.
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Coordinate System
A coordinate system provides a framework for locating points in space using ordered pairs or triples. In a two-dimensional Cartesian coordinate system, the x-axis represents the horizontal direction and the y-axis represents the vertical direction. This system is crucial for visualizing vectors and performing operations such as vector subtraction, as it allows for a clear understanding of the vectors' positions and directions.
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