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
2:05 minutes
Problem 4b
Textbook Question
Textbook QuestionIf P₁ = (-2, 3), P₂ = (-1, 5), and v is the vector from P₁ to P₂, Write v in terms of i and j.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Vectors
A vector is a mathematical object that has both magnitude and direction. In a two-dimensional space, a vector can be represented as an ordered pair of coordinates, indicating its position relative to a reference point. For example, the vector from point P₁ to P₂ can be calculated by subtracting the coordinates of P₁ from those of P₂.
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Unit Vectors i and j
In the Cartesian coordinate system, the unit vectors i and j represent the directions of the x-axis and y-axis, respectively. The vector i is typically represented as (1, 0), indicating movement along the x-axis, while j is represented as (0, 1), indicating movement along the y-axis. Any vector can be expressed as a linear combination of these unit vectors.
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i & j Notation
Vector Subtraction
Vector subtraction involves finding the difference between two vectors, which results in a new vector. For points P₁ and P₂, the vector v from P₁ to P₂ is calculated by subtracting the coordinates of P₁ from those of P₂. This operation not only gives the direction from P₁ to P₂ but also provides the components of the vector in terms of i and j.
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