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

R = ((Rx * unit vector x) +(Ry * unit vector y) +(Rz * unit vector z))+

Subject Index for all interactive diagrams - Math - Vector - Three-Dimensional Vector

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