Posts Tagged ‘unit’

Cross Product

Tuesday, October 27th, 2009

The Cross Product of Vectors

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Description

A detailed tutorial on the cross product of two vectors. Step by step tutorial including several examples of how to find the cross product for reference.

Overview

A cross product is very similar to a dot product. However, the result of a cross product is a vector, and the result of a dot product is a scalar. In mathematical terms, the cross product can be defined as \mathbf{a}\times\mathbf{b}=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\sin(\theta)\,\mathbf{n}. Theta represents the meausre of the angle between a and b, and n is a unit vector perpendicular to both a and b. The vector this forms is a right-handed system.

Unit Vector

Friday, October 23rd, 2009

Definition of a Unit Vector

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Description

A detailed tutorial on the unit vector. Step by step tutorial including several examples of the unit vector and how to solve it for reference.

Overview

In linear algebra, a unit vector is a vector that only has a length or magnitude of one. They are often used to indicate direction. There is a process used to create a unit vector, called normalizing a vector. When doing this, you must divide a vector of arbitrary length by its length. To normalize a vector with three points, you would use this formula:

<span style="font-size: x-small;">\mathbf{\hat{a}} = \frac{\mathbf{a}}{\left\|\mathbf{a}\right\|} = \frac{a_1}{\left\|\mathbf{a}\right\|}\mathbf{e_1} + \frac{a_2}{\left\|\mathbf{a}\right\|}\mathbf{e_2} + \frac{a_3}{\left\|\mathbf{a}\right\|}\mathbf{e_3}</span>

Quadrantal Angles

Friday, October 16th, 2009

How to Find Values of Quadrantal Angles

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Description

A detailed tutorial on how to find values of quadrantal angles. Step by step tutorial including several examples of finding values of quadrantal angles for reference.

Overview

Quadrantal angles have a terminal side coinciding with a coordinate axis. A trigonometric functional value of such an angle can be determined by the coordinates of the point where the terminal side intersects the unit circle. When on the unit circle, the Cartesian coordinate (x, y) cooresponds to (cos(&), sin(&)) on the unit circle.

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