Three-Dimensional Vector

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

Visits since 5-29-09: 50387

Interactagram.com uses third-party advertising companies to serve ads when you visit our website. These companies may use information (not including your name, address, email address, or telephone number) about your visits to this and other websites in order to provide advertisements about goods and services of interest to you. If you would like more information about this practice and to know your choices about not having this information used by these companies, click here.