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 7.15
Textbook Question
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.
<IMAGE>
c + d
![](/channels/images/assetPage/verifiedSolution.png)
1
Identify vectors \( \mathbf{c} \) and \( \mathbf{d} \) from the given image or description.
Sketch vector \( \mathbf{c} \) on a graph or coordinate plane, starting from an initial point.
From the same initial point, sketch vector \( \mathbf{d} \) to ensure both vectors have their initial points coinciding.
Use the parallelogram rule: complete the parallelogram by drawing lines parallel to \( \mathbf{c} \) and \( \mathbf{d} \) from the tips of each vector.
The diagonal of the parallelogram starting from the initial point represents the resultant vector \( \mathbf{c} + \mathbf{d} \).
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