Values used in physics are either **scalar** or **vector**.

Scalar values indicate positive magnitudes such as mass, speed, work, charge, or energy, and have no directional component.

Many values do, however, have a directional component. These includes **position**, **velocity**, **acceleration**, and **force**, which all require a vector to be described properly. See interactive diagram above.

For a three-dimensional vector, we can use three numbers to describe the end-point of a directed line segment that starts at the origin, with each number indicating the displacement along each of the three axis, the **x axis**, **y axis**, and **z axis**.

We can determine the length of such a vector with the equation:

length = sqrt(Rx2 + Ry2 + Rz2)

We can describe the direction of the vector in terms of two angles, where:

angle 1 = acos(Ry/length)

angle 2 = atan(Rx/Rz)

We can think of the vector **R** in the diagram as the sum of the unit vectors, each multiplied by the magnitude of **R** in each respective dimension (see green dots), or

Subject Index for all interactive diagrams

interactagram.com - Math - Vector - Three-Dimensional Vector

Source Flash: threeDVector.zip

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