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Calculus with Analytic Geometry
Calculus of a Single Variable
Multivariable Calculus, Seventh Edition
Ron Larson - The Pennsylvania State University, The Behrend
College
Robert P. Hostetler - The Pennsylvania State University, The Behrend College
Bruce H. Edwards - University of Florida | | |
| | Chapter Summary
Chapter 10: Vectors and Geometry in Space
10.1
- Write the component form of a vector.
- Perform vector operations and interrupt the results geometrically.
- Write a vector as a linear combination of standard unit vectors.
- Use vectors to solve problems involving force or velocity.
10.2
- Understand the three-dimensional rectangular coordinate system.
- Analyze vectors in space.
- Use three-dimensional vectors to solve real-life problems.
10.3
- Use properties of the dot product of two vectors.
- Find the angle between two vectors using the dot product.
- Find the direction cosines of a vector in space.
- Find the projection of a vector onto another vector.
- Use vectors to find the work done by a constant force.
10.4
- Find the cross product of two vectors in space.
- Use the triple scalar product of three vectors in space.
10.5
- Write a set of parametric equations for a line in space.
- Write a linear equation to represent a plane in space.
- Sketch the plane given by a linear equation.
- Find the distance between point, planes, and lines in space.
10.6
- Recognize and write equations for cylindrical surfaces.
- Recognize and write equations for quadratic surfaces.
- Recognize and write equations for surfaces of revolution.
10.7
- Use cylindrical coordinates to represent surfaces in space.
- Use spherical coordinates to represent surfaces in space.
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