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Example Vector

Example Vector in 3D

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

Below is the same simulation as the one previously of an example vector in the x, y, and z axis. It has a magnitude (length) of 5.385, and an angle of 33.8545 and its direction is northeast. Vectors portrayed in three dimensions have three vector components. This simulation rotates however, and as a student you will be able to change this vector's rotation, angle, direction, and magnitude.

Vector:

x, y, z:

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

\[ \vec{D} = \begin{bmatrix} \hat{i} & \hat{j} & \hat{k} \\ 4 & 2 & 3 \end{bmatrix} \]

or

\[ \vec{D} = 4\hat{i} + 2\hat{j} + 3\hat{k} \]

or

\[ \vec{D} = \langle 4, 2, 3 \rangle \]

This vector has a length (magnitude) of 5.385. When you look at the directions of the vector, it starts at (0, 0, 0) and ends on (4, 2, 3). This means that this vector's vector components are positive 4 on the x-axis, positive 2 on the y-axis, and positive 3 on the z-axis. These vector components would change if the vector had a different magnitude, angle, and direction.

You have now learned the fundamentals of what makes a vector a vector. Go back now to the vector page to move onto the next lesson.

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