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| Addition or Composition of Vectors |
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| Scalars can be added algebraically. However, vectors do not obey the ordinary laws of algebra. This is because vectors possess both magnitude and direction. Vectors are added geometrically. The process of adding two or more vectors is known as addition or composition of vectors. When two or more vectors are added, the result is a single vector called the resultant vector. |
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| The resultant of two or more vectors is that single vector which alone produces the same effect as that produced by the two individual vectors. |
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| Three laws have been evolved for the addition of vectors: |
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 Triangle law of vectors for addition of two vectors. |
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 Parallelogram law of vectors for addition of two vectors. |
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 Polygon law of vectors for addition of more than two vectors. |
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Let a particle be at the points A, B, C
at three successive times t, t' and t'' respectively. 
is the displacement vector from time t to t'. 
is the displacement vector from time t' to t''. The
total displacement vector  is the sum or the
resultant of individual displacement vector 
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| This leads to the statement of the law of triangle of vectors. |
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| If two vectors can be represented both in magnitude and direction by the two sides of a triangle taken in the same order, then the resultant is represented completely, both in magnitude and direction, by the third side of the triangle taken in the opposite order. |
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It follows from triangle law of vectors
that, if three vectors are represented by the three sides of a triangle
taken in order, then their resultant is zero. Thus, if three vectors 
can be represented completely by the three sides of a triangle taken in
order, then their vector sum is zero. |
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| If the resultant of three vectors is zero, then these can be represented completely by the three sides of a triangle taken in order. |
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Let two vectors  acting simultaneously on a particle be represented both in magnitude and direction, by the sides OA and AC of a triangle OAC, taken in order, as shown in the figure. Applying
triangle law of vectors, we find that the resultant
 of
the given vectors can be represented by the side OC
of the triangle. |
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| In the right angled DONC, considering the magnitudes only |
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| Equation |
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| In the right angled DANC, |
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| Substituting for NC and AN in equation (1), we have |
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| The above equation (2) gives the magnitude of the resultant vector |
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| The same equation (2) can also be expressed in the following ways |
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The direction of the resultant can be determined by calculation of b,
which is the angle that  |
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 from the right-angled DONC, |
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