Difference between revisions of "ModelCourses/Calculus/Vectors/Vectors in Space"
Jump to navigation
Jump to search
| Line 5: | Line 5: | ||
** 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 16:42, 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
