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Addition of Vectors by Analytical Method Parallelogram Law

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Addition of Vectors by Analytical Method Parallelogram Law - Lesson Summary

The Parallelogram Law helps us to find the magnitude and direction of the resultant vector C, which is the vector sum of two vectors A and B.

Consider two vectors A and B passing through a point O. The angle between them is θ. To find the resultant C of these two vectors, complete the parallelogram with A and B as adjacent sides. The diagonal drawn from O of the parallelogram represents the resultant C of the two given vectors A and B. The resultant vector C makes an angle α with vector A.

This equation is known as the Law of Cosines. Using this, we can find the magnitude of the resultant vector. The direction of the resultant vector is given by the following equation:

            tan α = B sin θ A + B cos θ  


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