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Example Vector

Example Vector in 2D

A Vector is an object that has a three properties: a magnitude (length), a direction, and an angle.

Below is a simulation of an example vector in the x and y axis. It has a magnitude (length) of 20, and a variable angle and direction based on the movement of your mouse. Vectors portrayed in two dimensions have two vector components.

A vector can be represented in numerous ways. Here are the three most common ways of portraying them:

\[ \vec{C} = \begin{bmatrix} \hat{i} & \hat{j} & \hat{k} \\ 16 & 12 & 0 \end{bmatrix} \]

or

\[ \vec{C} = 16\hat{i} + 12\hat{j} + 0\hat{k} \]

or

\[ \vec{C} = \langle 16, 12, 0 \rangle \]

This vector has a length (magnitude) of 20. When you look at the directions of the vector, it starts at (0,0) and ends on any point you move your mouse on. As you move your mouse arrow over the simulation you can see how vector components change when the angle and direction are changed only, as long as the vector would have a magnitude of 20. Later on you will see how vector components change if you change all three: the magnitude, angle, and direction.

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