# Explain scalar and vector quantities. Write a way to express a vector. Define unit vector.

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Explain scalar and vector quantities. Write a way to express a vector. Define unit vector.

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Scalar and vector quantities: The physical quantities which have only magnitude and need no idea of direction are called scalar quantities.

For example: Speed, mass, time, length, area, volume, density, work, energy etc.

Vector quantities: There are certain quantities which require magnitude as well as direction, to express them clearly, i.e., the physical quantities which have magnitude, as well as direction, are called vector quantities.

For example: Velocity, acceleration, force, pressure etc.

Vector representation: A vector quantity is represented by a single arrow. It is written as $\bar { AB }$. Here, length of AB is the magnitude of |$\bar { AB }$|.

Unit Vector

A unit vector is a vector whose magnitude is unit and direction is the direction of the vector, say $\bar { AB }$. A unit vector is denoted by $\hat { A }$ and it is read as A cap.
$\bar{A} =|\bar{A}|\hat {A} =\hat{A} =\frac{\bar{A}}{|\bar{A}|}$