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Example Vector

Example Vector in 1D x-axis

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-axis. It has a magnitude (length) of 10, and a variable angle of 0 or 180 degrees, and a variable direction of east or west, both based on the movement of your mouse. Vectors portrayed in the first dimension can also be looked upon as vector components because the vector does not intersect with other axis planes, making the other vector components equal 0.

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

\[ \vec{A} = \begin{bmatrix} \hat{i} & \hat{j} & \hat{k} \\ 10 & 0 & 0 \end{bmatrix} \]

\[ \vec{A} = \begin{bmatrix} \hat{i} & \hat{j} & \hat{k} \\ -10 & 0 & 0 \end{bmatrix} \]

or

\[ \vec{A} = 10 \hat{i} + 0 \hat{j} + 0 \hat{k} \]

\[ \vec{A} = -10 \hat{i} + 0 \hat{j} + 0 \hat{k} \]

or

\[ \vec{A} = \langle 10, 0, 0 \rangle \]

\[ \vec{A} = \langle -10, 0, 0 \rangle \]

This vector has a (magnitude) of 10, however when you move your mouse over the simulation, the vector changes its direction. As a result of this, the vector has diffrerent components: one positive, one negative. This means that this vector's vector components can be either +10 or -10.

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