ModelCourses/Calculus/Vectors/Vectors in Space: Difference between revisions
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* Dot Product and Applications | * Dot Product and Applications | ||
** Two definitions of dot product of two vectors | ** Two definitions of dot product of two vectors | ||
** Angle | ** Angle between two vectors | ||
*** | *** Compute the dot product of two vectors. | ||
*** | *** Compute the angle between two vectors. | ||
*** | *** Determine if two vectors are parallel or orthogonal (perpendicular) when the cosine of the angle between these two vector is 1, -1, or 0. | ||
*** | *** Determine if the angle between two vectors is acute or obtuse when the dot product of these two vectors is positive or negative. | ||
*** | *** Create a vector v that is parallel to a given vector. | ||
*** | *** Create a vector v that is orthogonal to a given vector. | ||
*** Given a vector u and an angle theta, create a vector v such that the angle | *** Given a vector u and an angle theta, create a vector v such that the angle between u and v is theta. | ||
** Projection of vector u onto vector v | ** Projection and component of vector u onto vector v | ||
*** | *** Compute the work done by a force vector along a direction vector. | ||
*** Compute the distance from a given point to a given line. | |||
*** Compute the distance between two planes. | |||
* Cross Product and Applications | * Cross Product and Applications | ||
Revision as of 21:36, 23 December 2011
Vectors in Space
- Vector Algebra
- The right-handed coordinate system, three axes, three coordinate planes and eight octants
- Sketch a point in space.
- Sketch a line that passes through a given point and is parallel to an axis.
- Sketch a plane that contains a point and is parallel to a coordinate plane.
- Sketch a plane that contains a point and is perpendicular to an axis.
- Express a vector from Point A to Point B in vector notation.
- Sketch a position vector.
- Vector algebra: (1) scalar multiplication; (2) vector addition and subtraction
- Compute and sketching a scalar times a vector and a sum (difference) of two vectors.
- Triangle inequality
- The right-handed coordinate system, three axes, three coordinate planes and eight octants
- Dot Product and Applications
- Two definitions of dot product of two vectors
- Angle between two vectors
- Compute the dot product of two vectors.
- Compute the angle between two vectors.
- Determine if two vectors are parallel or orthogonal (perpendicular) when the cosine of the angle between these two vector is 1, -1, or 0.
- Determine if the angle between two vectors is acute or obtuse when the dot product of these two vectors is positive or negative.
- Create a vector v that is parallel to a given vector.
- Create a vector v that is orthogonal to a given vector.
- Given a vector u and an angle theta, create a vector v such that the angle between u and v is theta.
- Projection and component of vector u onto vector v
- Compute the work done by a force vector along a direction vector.
- Compute the distance from a given point to a given line.
- Compute the distance between two planes.
- Cross Product and Applications
- Computation of the cross product of two vectors
- The cross product of vectors u and v is orthogonal (perpendicular) to u and v
- Given two vectors u and v that are not parallel, find a vector which is orthogonal to both u and v
- Given two vectors, determine a vector which is normal