ModelCourses/Calculus/Vectors/Vectors in Space: Difference between revisions
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* Vector Algebra | * Vector Algebra | ||
** | |||
** Expressing a vector from Point A to Point B in vector notation | ** Expressing a vector from Point A to Point B in vector notation | ||
** 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 | ||
*** 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 | ||
** Triangle inequality | ** Triangle inequality | ||
* 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 | ||
** Angle of two vectors | ** Angle of two vectors | ||
| Line 15: | Line 16: | ||
*** 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 | ||
*** 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 | ||
*** 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 | |||
*** Work done by a force vector along a direction vector | |||
* 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 | ||
** Orthogonality | ** Orthogonality | ||
Revision as of 23:32, 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