The parallelogram law of vectors states that if two vectors acting simultaneously at a point can be represented in magnitude and direction by two adjacent sides of a parallelogram drawn from a point, then their resultant vector is represented in magnitude and direction by the diagonal of the parallelogram originating from the same point.
Mathematically, if we have two vectors A and B acting at a point P, then the resultant vector R can be found using the parallelogram law:
R = A + B
To visually represent this law, we draw the vectors A and B as sides of a parallelogram with P as one of the vertices. The resultant vector R is represented by the diagonal of the parallelogram originating from P.
The magnitude of the resultant vector R can be found using the law of cosines:
|R| = sqrt(|A|^2 + |B|^2 + 2|A||B|cosθ)
where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.
The direction of the resultant vector R can be found using the law of sines:
sin(α) / |A| = sin(θ) / |R|
where α is the angle between the resultant vector R and vector A.
The parallelogram law of vectors is widely used in physics and engineering to find the net effect of multiple forces acting on an object or the result of adding multiple velocity vectors.
Parallelogram law of vectors
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