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Published byRalph Caldwell Modified about 1 year ago

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SCALARS AND VECTORS

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Scalar is a simple physical quantity that is not changed by coordinate system rotations or translations. Expressing a scalar quantity we give it simply with a number and a unit (for example, 12 kg). If a quantity has both a magnitude and direction, it is called a vector.

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SCALARS AND VECTORS Scalars (magnitude)Vectors (magnitude+direction) SpeedVelocity TemperatureAcceleration DistanceDisplacement AreaForce EntropyMomentum VolumeThe electric field intensity Etc

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Vectors Vectors are equal when they have the same magnitude and direction, irrespective of their point of origin. A A A

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SUM OF TWO VECTORS A B C= A + B B If two vectors have the same direction, their resultant has a magnitude equal to the sum of their magnitudes and will also have the same direction.

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SUM OF TWO VECTORS A B C= A + B B If two vectors have the opposite direction, their resultant has a magnitude equal to the subtraction of their magnitudes; direction of the sum is equivalent to the direction of longer vector (to the bigger magnitude).

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SUM OF TWO VECTORS BY A GRAPHICAL METHOD A B B C=A+B Two vectors A and B are added by drawing the arrows which represent the vectors in such a way that the initial point of B is on the terminal point of A. The resultant C = A + B, is the vector from the initial point of A to the terminal point of B.

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Polygon method

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Parallelogram method In the parallelogram method for vector addition, the vectors are translated, (i.e., moved) to a common origin. The resultant R is the diagonal of the parallelogram drawn from the common origin.

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Method of components The components of a vector are those vectors which, when added together, give the original vector. The sum of the components of two vectors is equal to the sum of these two vectors.

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Rectangular components In all vector problems a natural system of axes presents itself. In many cases the axes are at right angles to one another. Components parallel to the axes of a rectangular system of axes are called rectangular components. In general it is convenient to call the horizontal axis X and the vertical axis Y. The direction of a vector is given as an angle counter-clockwise from the X-axis.

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Rectangular components

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Multiplication of vectors by positive scalar Scalar multiplication of vector by a positive real number multiplies the magnitude of the vector without changing its direction. a 2a 3a

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Multiplication of vectors by negative scalar Scalar multiplication of vector by a negative real number multiplies the magnitude of the vector and changes its direction into opposite directions. a -2a -3a

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Division of vectors by scalars Scalar dividing of vector by a real number is equal to multiplication with reciprocal (or multiplicative inverse) of that number. a a÷2 = ½ x a b b÷(-3) = -1/3 x b

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