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Scalars and Vectors

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Scalars and Vectors - Lesson Summary

Rectilinear motion is a motion that occurs in a straight line. The motion of a body in a straight line is treated as one-dimensional motion. The description of motion of a body involves its position, displacement, velocity, acceleration and time. In the straight-line motion of a body, we can represent all these entities on a number line.

The motion of a body in a plane is two-dimensional and is described using the vector representation. For doing this one should learn the basics of scalars and vectors. Quantities that are described completely with the help of a number along with its unit are called scalars. Scalars have only magnitude. Mass, distance, temperature and time are scalars. As with numbers in elementary mathematics, scalars can be added, subtracted, multiplied and divided.



Quantities that require specification of the line of action or direction in addition to their magnitude to complete their description are called vectors. A vector is always specified by its magnitude and its direction. Displacement, velocity, acceleration and force are vectors. Vectors are represented by a straight line with an arrowhead. The length of the line drawn to some suitable scale represents magnitude and the line itself with the arrow represents direction. Vectors of a given physical quantity can be added only by using the triangle law of addition or the parallelogram law of addition.


 
The position vector of an object moving in a plane is the vector that represents the position of the object at a particular instant.    OA and OA’ are the position vectors of the object at time t and t’, and their magnitudes r and r’, respectively. AA’ is the displacement vector for the motion of the object from point A to A’. The displacement vector is obtained only from the initial and final positions of the object. It is independent of the path followed by the object.

Two vectors P and Q  are said to be equal only if they have the same magnitude and the same direction.

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