The parallelogram law of vectors is a fundamental principle in vector algebra. It states that if two vectors \( \mathbf{A} \) and \( \mathbf{B} \) are represented as adjacent sides of a parallelogram, then the diagonal of the parallelogram that starts from the same point as the two vectors represents the sum, \( \mathbf{A} + \mathbf{B} \), of the two vectors.
Mathematically, it can be expressed as:
\[ \mathbf{A} + \mathbf{B} = \mathbf{R} \]
where \( \mathbf{R} \) is the resultant vector (the diagonal of the parallelogram).
To visualize, suppose you have two vectors \( \mathbf{A} \) and \( \mathbf{B} \) drawn with a common initial point. If you complete the parallelogram by drawing lines parallel to these vectors, the diagonal starting from the common initial point of \( \mathbf{A} \) and \( \mathbf{B} \) will give you the resultant vector \( \mathbf{R} \).
This law is often used in physics and engineering to determine the resultant of two forces, velocities, or other vector quantities.
State the parallelogram law of vector
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