Difference between revisions of "ModelCourses/Calculus/Vectors/Vectors in Space"
Jump to navigation
Jump to search
| Line 10: | Line 10: | ||
* The Dot Product of Two Vectors |
* The Dot Product of Two Vectors |
||
** Two definitions of dot product of two vectors |
** Two definitions of dot product of two vectors |
||
| + | ** Angle of two vectors |
||
*** Computing the dot product of two vectors |
*** Computing the dot product of two vectors |
||
*** Computing the angle between two vectors |
*** Computing the angle between two vectors |
||
| − | *** Determining two vectors are parallel or orthogonal (perpendicular) |
+ | *** Determining if two vectors are parallel or orthogonal (perpendicular) when cosine of the angle is 1, -1, or 0 |
| − | *** Determining the angle |
+ | *** Determining if the angle of two vectors is acute, or obtuse when the dot product of two vectors is positive or negative |
| − | ** 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 |
||
| − | ** Angle between vectors, orthogonality and cos(theta) |
||
| + | *** Given a particular vector, create other orthogonal vectors of desired length |
||
| − | *** 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 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 |
||
* The Cross Product of Two Vectors in Space |
* The Cross Product of Two Vectors in Space |
||
Revision as of 18:52, 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 subtraction
- Computing and sketching a scalar times a vector and a sum (difference) of two vectors
- Triangle inequality
- The Dot Product of Two Vectors
- Two definitions of dot product of two vectors
- Angle of two vectors
- Computing the dot product of two vectors
- Computing the angle between two vectors
- Determining if two vectors are parallel or orthogonal (perpendicular) when cosine of the angle is 1, -1, or 0
- Determining if the angle of two vectors is acute, or obtuse when the dot product of two vectors is positive or negative
- Given a particular vector, create other parallel vectors of desired length
- Given a particular vector, create other orthogonal vectors of desired length
- Given one vector and an angle, determine another other vector with the desired angle. Maybe give part of the second vector.
- 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
