Addition and Subtraction Of Vectors (Analytical Method)

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Addition Of Vectors (Analytical Method)

Let we consider two vectors A and B inclined at an angle θ. Let they may be represented in magnitude and direction by two sides OP and PQ of ∆OPQ, taken in same order. Then, according to Triangle Law of vector addition, the resultant R is given by the closing side OQ, taken in opposite order.

Addition Of Vectors (Analytical Method)
Addition Of Vectors (Analytical Method)
Addition Of Vectors (Analytical Method)
Addition Of Vectors (Analytical Method)

If the resultant vector R makes an angle β with the direction of vector A, then from ∆QNO,

Addition Of Vectors (Analytical Method)
Addition Of Vectors (Analytical Method)
Addition Of Vectors (Analytical Method)
Addition Of Vectors (Analytical Method)

Subtraction Of Vectors (Analytical Method)

If there are two vectors A and B at angle θ. If we have to subtract B from A, then first invert the vector B and add with vector A.

Subtraction Of Vectors (Analytical Method)
Subtraction Of Vectors (Analytical Method)

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