ModelCourses/Calculus/Vectors/Vectors in Space: Difference between revisions
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** Sketching a position vector | ** Sketching a position vector | ||
** Vector algebra: (1) scalar multiplication; (2) vector addition and substraction | ** Vector algebra: (1) scalar multiplication; (2) vector addition and substraction | ||
** | ** Magnitude and 2-norm of a vector, unit vector | ||
** | ** Triangle inequality | ||
* The Dot Product of Two Vectors | * The Dot Product of Two Vectors | ||
** Calculating the standard collection of numerical examples | ** Two definitions of dot product of two vectors | ||
*** Calculating the standard collection of numerical examples | |||
** Parallel and geometric implications | ** Parallel and geometric implications | ||
*** Given a particular vector, create other parallel vectors of desired length | *** Given a particular vector, create other parallel vectors of desired length | ||
| Line 16: | Line 17: | ||
*** Given one vector and an angle, determine another other vector with the desired angle. Maybe give part of the second vector. | *** Given one vector and an angle, determine another other vector with the desired angle. Maybe give part of the second vector. | ||
*** Given one 2d vector, determine another vector which is orthogonal | *** Given one 2d vector, determine another vector which is orthogonal | ||
* The Cross Product of Two Vectors in Space | * The Cross Product of Two Vectors in Space | ||
** Calculating the standard collection of numerical examples | ** Calculating the standard collection of numerical examples | ||
Revision as of 21:42, 21 December 2011
Vectors in Space
- Vector Algebra
- Expressing a vector from Point A to Point B in vector notation
- Sketching a position vector
- Vector algebra: (1) scalar multiplication; (2) vector addition and substraction
- Magnitude and 2-norm of a vector, unit vector
- Triangle inequality
- The Dot Product of Two Vectors
- Two definitions of dot product of two vectors
- Calculating the standard collection of numerical examples
- Parallel and geometric implications
- Given a particular vector, create other parallel vectors of desired length
- Angle between vectors, orthogonality and cos(theta)
- Given two vectors, determine the angle between
- Given one vector and an angle, determine another other vector with the desired angle. Maybe give part of the second vector.
- Given one 2d vector, determine another vector which is orthogonal
- Two definitions of dot product of two vectors
- The Cross Product of Two Vectors in Space
- Calculating the standard collection of numerical examples
- Orthogonality
- Given a vector, determine another vector which is orthogonal
- Orthogonality between three vectors
- Given two vectors, determine a vector which is normal