what is parallelogram law of vector addition ??
explain !!
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what is parallelogram law of vector addition ??
explain !!
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According to the parallelogram law of vector addition if two vectors act along two adjacent sides of a parallelogram(having magnitude equal to the length of the sides) both pointing away from the common vertex, then the resultant is represented by the diagonal of the parallelogram passing through the same common vertex ...
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Parallelogram law states that the sum of the squares of the length of the four sides of a parallelogram is equal to the sum of the squares of the length of the two diagonals. In Euclidean geometry, it is necessary that the parallelogram should have equal opposite sides.
If ABCD is a parallelogram, then AB = DC and AD = BC. Then according to the definition of the parallelogram law, it is stated as
2(AB)2 + 2 (BC)2 = (AC)2 + (BD)2.
In case the parallelogram is a rectangle, then the law is stated as:
2(AB)2 + 2 (BC)2 = 2(AC)2
Because in rectangle, two diagonals are of equal lengths. i.e., (AC = BD)
If two vectors are acting simultaneously at a point, then it can be represented both in magnitude and direction by the adjacent sides drawn from a point. Therefore, the resultant vector is completely represented both in direction and magnitude by the diagonal of the parallelogram passing through the point.
According to the parallelogram law, the side OC of the parallelogram represents the resultant vector R.
OA→+OB→=OC→ (or)
P⃗ +Q⃗ =R⃗
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