Difference between revisions of "ModelCourses/Calculus/Vectors/Vectors in Space"
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* Vector Algebra |
* Vector Algebra |
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| + | ** |
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** Expressing a vector from Point A to Point B in vector notation |
** Expressing a vector from Point A to Point B in vector notation |
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| − | ** Sketching a position vector |
+ | *** Sketching a position vector |
** Vector algebra: (1) scalar multiplication; (2) vector addition and subtraction |
** Vector algebra: (1) scalar multiplication; (2) vector addition and subtraction |
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*** Computing and sketching a scalar times a vector and a sum (difference) of two vectors |
*** Computing and sketching a scalar times a vector and a sum (difference) of two vectors |
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** Triangle inequality |
** Triangle inequality |
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| − | * The Dot Product of Two Vectors |
+ | * The Dot Product of Two Vectors and Applications |
** Two definitions of dot product of two vectors |
** Two definitions of dot product of two vectors |
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** Angle of two vectors |
** Angle of two vectors |
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*** Determining if two vectors are parallel or orthogonal (perpendicular) when cosine of the angle is 1, -1, or 0 |
*** Determining if two vectors are parallel or orthogonal (perpendicular) when cosine of the angle is 1, -1, or 0 |
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*** Determining if the angle of two vectors is acute, or obtuse when the dot product of two vectors is positive or negative |
*** Determining if the angle of two vectors is acute, or obtuse when the dot product of two vectors is positive or negative |
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| − | *** Given a |
+ | *** Given a vector u, create a vector that is parallel to u |
| − | *** Given a |
+ | *** Given a vector u, create a vector that is orthogonal to u |
| − | *** Given |
+ | *** Given a vector u and an angle theta, create a vector v such that the angle of u and v is theta |
| + | ** Projection of vector u onto vector v |
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| + | *** Work done by a force vector along a direction vector |
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| − | * The Cross Product of Two Vectors in Space |
+ | * The Cross Product of Two Vectors in Space and Applications |
** Calculating the standard collection of numerical examples |
** Calculating the standard collection of numerical examples |
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** Orthogonality |
** Orthogonality |
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Revision as of 19:32, 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
- Expressing a vector from Point A to Point B in vector notation
- The Dot Product of Two Vectors and Applications
- 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 vector u, create a vector that is parallel to u
- Given a vector u, create a vector that is orthogonal to u
- Given a vector u and an angle theta, create a vector v such that the angle of u and v is theta
- Projection of vector u onto vector v
- Work done by a force vector along a direction vector
- The Cross Product of Two Vectors in Space and Applications
- 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
