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 7.7
Textbook Question
Textbook QuestionCONCEPT PREVIEW Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Vector Addition
Vector addition involves combining two or more vectors to determine a resultant vector. This can be done graphically by placing the tail of one vector at the head of another, or by using the parallelogram rule, where two vectors are represented as adjacent sides of a parallelogram, and the diagonal represents the resultant.
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Parallelogram Rule
The parallelogram rule is a method for finding the resultant of two vectors. By drawing the two vectors as adjacent sides of a parallelogram, the diagonal from the common initial point to the opposite corner represents the resultant vector in both magnitude and direction.
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Sketching Vectors
Sketching vectors accurately is crucial for visualizing vector addition and understanding their relationships. Each vector is represented by an arrow, where the length indicates magnitude and the direction of the arrow indicates the vector's direction. Properly sketching vectors helps in applying the parallelogram rule effectively.
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