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How are vectors added using the parallelogram rule?
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linear algebra
One method of adding and subtracting vectors is to place their tails together and then supply two more sides to form a parallelogram. The vector from their tails to the opposite corner of the parallelogram is equal to the sum of the original vectors. The vector between their heads (starting from the vector being subtracted) is equal to their difference.
To add two vectors, v and w, using the parallelogram rule, you first move both vectors so that they originate from the same point (the origin). Once positioned, you use these two vectors as adjacent sides to construct a parallelogram.12
The sum of the two vectors, v + w, is represented by the diagonal vector that extends from the common starting point to the opposite vertex of the parallelogram. This geometric construction is a fundamental method in vector analysis for finding the resultant of two vector quantities.123