# Vector Diagram

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## Vector Diagram

a graphical representation of the values of periodically varying quantities and the relationships between them by means of directed line segments called vectors.

Vector diagrams are widely used in electrical engineering, acoustics, optics, and other areas of science. The simple harmonic functions of one period, for example,

*f*_{1} = *B*_{1} sin ω*t*

*f*_{2} = *B*_{2} sin (α+ω*t*)

*f*_{3} = *B*_{3} sin (β+ω*t*)

can be represented graphically (see Figure 1) as projections on the *O _{y}* axis of vectors

**OA**

_{1}

**OA**

_{2}, and

**OA**

_{3}rotating with constant angular velocity ω, while

**OA**

_{2}and

**OA**

_{3}are turned by the angles

*α*and

*β*with reference to

**OA**

_{1}. The length of the vectors corresponds to the amplitude of the oscillation:

The sum or difference of two or more oscillations is indicated on a vector diagram as the geometric sum or difference of the vectors of the component oscillations, obtained according to the parallelogram rule, and the instantaneous value of the unknown quantity is determined by the projection of the vector sum on the *O _{y}* axis.

For example, it is required to find the sum *F* of the oscillations f_{l} with amplitude **OA**_{1} and *f*_{2}, with amplitude **OA**_{2}. By the geometric addition of vectors **OA**_{1} and **OA**_{2} on the vector diagram, we find that the amplitude of the summed oscillation *F* is equal to the length of vector **OC** = **OA**_{1} + **OA**_{2} and leads the oscillation *f*_{1} in phase by the angle *φ*