Posts Tagged ‘direction’
Thursday, November 12th, 2009
How to Draw Best-Fitting Lines
Description
A detailed tutorial on how to draw best-fitting lines. Step by step tutorial including several examples on how to draw best-fitting lines for reference.
Overview
Best-fitting lines are lines that are drawn on a graph or on scatter plots. However, a best-fitting line is different than a normal line found on a graph. A normal graph simply requires you to connect the dots. A best fitting line focuses not on what dots to connect, but how to connect them. The line will curve or go in different directions, not just straight to the other line, depending on the relationship of the two dots to each other. Best-fitting lines typically require more information than simply the graph, you must explore the equation and each point to find the true relationships, and from that you can find the best-fitting line.
Tags: algebra, best, best-fitting, connect, coordinate, curve, direction, dots, equation, fitting, graph, line, plot, points, relationship, scatter, straight
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Tuesday, October 27th, 2009
Definition of a Null Vector
Description
A detailed tutorial on the definition of a null vector. Step by step tutorial including several examples of null vectors for reference.
Overview
A null vector is a vector that has no direction. It is placed at the coordinates (0, 0, 0) in Euclidean space. Another name for a null vector is a zero vector. Although the null vector is the only vector that has no direction, we cannot say that the null vector is unique because more than one vector has the possibility of being null.
Tags: 0, algebra, arrow, coordinates, direction, Euclidean, length, magnitude, null, space, vector, zero
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Tuesday, October 27th, 2009
Introduction to Vector Equality
Description
A detailed tutorial on how to determine if two vectors are equal. Step by step tutorial including several examples of vector equality for reference.
Overview
Vectors are said to be equal if they have the same magnitude and direction. They must also have the same coordinates. Using this logic, it is possible to determine if you have two vectors 
and 
, they are equal if 
.
Tags: a, algebra, b, coordinates, direction, E, equal, equality, length, magnitude, vector
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Tuesday, October 27th, 2009
Overview of Euclidean Vectors
Description
A detailed tutorial on Euclidean vectors. Step by step tutorial including several examples and visual examples of Euclidean vectors for reference.
Overview
A vector is a geometric object that has both a magnitude (also known as the length) and a direction. They are usually drawn as arrows that have a similar starting point and connect two points together. The difference between different kinds of vectors is what coordinate system is used to describe them. Euclidean vectors are vectors that are described by the Cartesian coordinate system.
Tags: algebra, arrow, cartesian, coordinate, direction, Euclidean, geometric, graph, initial, length, magnitude, point, system, terminal, vector
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Friday, October 23rd, 2009
Definition of a Unit Vector
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:
Tags: algebra, arbitrary, direction, formula, length, magnitude, normalizing, one, point, unit, vector
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Friday, October 23rd, 2009
Overview of the Dot Product
Description
A detailed tutorial of the dot product. Step by step tutorial including several examples of the dot product of a vector for reference.
Overview
The dot product of two vectors always ends up being a scalar. In mathematical terms, this is ![<span style="font-size: x-small;">\mathbf{a}\cdot\mathbf{b}=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\cos\theta[</span>/latex]. In this case, theta is the measure of the angle between a and b. The definition of a dot product given geometrically is that a and b have a common starting point and that the length of a is multiplied by the component in b that points in the same direction as a. Algebraically, it can be said that [latex]<span style="font-size: x-small;">\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3.</span>](http://s.wordpress.com/latex.php?latex=%3Cspan%20style%3D%22font-size%3A%20x-small%3B%22%3E%5Cmathbf%7Ba%7D%5Ccdot%5Cmathbf%7Bb%7D%3D%5Cleft%5C%7C%5Cmathbf%7Ba%7D%5Cright%5C%7C%5Cleft%5C%7C%5Cmathbf%7Bb%7D%5Cright%5C%7C%5Ccos%5Ctheta%5B%3C%2Fspan%3E%2Flatex%5D.%20In%20this%20case%2C%20theta%20is%20the%20measure%20of%20the%20angle%20between%20a%20and%20b.%20The%20definition%20of%20a%20dot%20product%20given%20geometrically%20is%20that%20a%20and%20b%20have%20a%20common%20starting%20point%20and%20that%20the%20length%20of%20a%20is%20multiplied%20by%20the%20component%20in%20b%20that%20points%20in%20the%20same%20direction%20as%20a.%20Algebraically%2C%20it%20can%20be%20said%20that%20%5Blatex%5D%3Cspan%20style%3D%22font-size%3A%20x-small%3B%22%3E%5Cmathbf%7Ba%7D%20%5Ccdot%20%5Cmathbf%7Bb%7D%20%3D%20a_1%20b_1%20%2B%20a_2%20b_2%20%2B%20a_3%20b_3.%3C%2Fspan%3E&bg=ffffff&fg=000000&s=0 "<span style=\"font-size: x-small;\">\mathbf{a}\cdot\mathbf{b}=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\cos\theta[</span>/latex]. In this case, theta is the measure of the angle between a and b. The definition of a dot product given geometrically is that a and b have a common starting point and that the length of a is multiplied by the component in b that points in the same direction as a. Algebraically, it can be said that [latex]<span style=\"font-size: x-small;\">\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3.</span>")
Tags: algebra, algebraically, angle, common, component, cosine, direction, dot, geometrically, initial, inner, length, mulitplied, point, product, scalar, starting, vector
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Friday, October 23rd, 2009
How to Solve Vectors Using Scalar Multiplication
Description
A detailed tutorial on how to solve vectors using scalar multiplication. Step by step tutorial including several examples on scalar multiplication for reference.
Overview
Scalar multiplication is when you multiply, or re-scale, vectors by a real number. These real numbers are referred to as scalars, so that they can be distinguished from vectors. So, scalar multiplication is when you multiply a vector by a scalar. When you multiply a scalar and a vector, you will get another vector. Your resulting vector will be:
When a vector is multiplied by a scalar, the vector is getting stretched out by a factor of the scalar. If the scalar is negative, then the vector changes direction. A property of scalar multiplication is that it is distributive.
Tags: algebra, direction, distributive, flippied, multiplication, multiply, negatve, number, property, real, rescale, scalar, stretched, vector
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Friday, October 23rd, 2009
How to Solve Vectors Using Vector Subtraction
Description
A detailed tutorial on how to solve vectors using vector subtraction. Step by step tutorial including several examples of vector subtraction for reference.
Overview
Vector subtraction involves two vectors that do not have to be equal, and could have different magnitudes and directions. The vectors are referred to as a and b. The formula for vector subtraction is:
In general, vector subtraction is defined geomtrically instead of algebraically, so it is not used quite as often as vector addition is.
Tags: addition, algebra, algebraically, direction, equal, formula, geometrically, Geometry, magnitude, subtraction, vector
Posted in Algebra | No Comments »
Friday, October 23rd, 2009
How to Solve Vectors Using Vector Addition
Description
A detailed tutorial on how to solve vectors using vector addition. Step by step tutorial including several examples of vector addition for reference.
Overview
Vector addition involves two vectors that do not have to be equal, and could have different magnitudes and directions. The vectors are referred to as a and b. The formula for vector addition is:
Vector addition is also occassionally referred to as the parallelogram rule, because on a picture diagram of vector addition the shape of a parallelogram is formed.
Tags: addition, algebra, direction, equal, formula, graph, magnitude, parallelogram, picture, rule, vector
Posted in Algebra | No Comments »
