Description
A detailed tutorial on the definition of a terminal point. Step by step tutorial including several examples of terminal points for reference.
Overview
A terminal point is just a way of saying the ending point. The terminal point of a line or a figure is the point where it ends. The term terminal point is used often when talking about vectors – they end at the terminal point. The terminal point is referred as the head of the vector.
Description
A detailed tutorial on the definition of an initial point. Step by step tutorial including several examples of initial points for reference.
Overview
An initial point is just a way of saying the starting point. The initial point of a line or a figure is the point where it begin. The term initial point is used often when talking about vectors – they start at the initial point. The initial point is referred as the tail of the vector.
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.
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
Description
A detailed tutorial on the intial side of an angle. Step by step tutorial including several examples of the initial side of an angle for reference.
Overview
The initial side of an angle is the side of an angle where the measurement begins. An angle is always measured from the degree of zero to the degree of the angle, regardless of if the angle is positive or negative. The best display of an initial side would be when you draw angles with a protractor – the line that you trace along the bottom of your protractor forms a ray which is known as the initial side.
Description
A detailed tutorial on the terminal side of an angle. Step by step tutorial including several examples of the terminal side of an angle for reference.
Overview
The terminal side of an angle is the side of an angle where the measurement ends. An angle is always measured from the degree of zero to the degree of the angle, regardless of if the angle is positive or negative. The best display of a terminal side would be when you draw angles with a protractor – the line that you draw for your degree forms a ray which is known as the terminal side.
![<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>")
