What are Scalars and Vectors?
Physical quantities are generally divided into two kinds called scalars and vectors. These two categories can be distinguished from one another by their distinct definitions:
Scalars are quantities that are fully described by a magnitude (or numerical value) alone. means A scalar is a number which expresses quantity. Scalars may or may not have units associated with them. Examples: mass, volume, energy, money
Vectors are quantities that are fully described by both a magnitude and a direction. means A vector is a quantity which has both magnitude and direction. The magnitude of a vector is a scalar. Examples: Displacement, velocity, acceleration, electric field
Properties of Scalar Quantities:
Physical quantities which can completely be specified by a number (magnitude) having an appropriate unit are known as “SCALAR QUANTITIES”.
- Scalar quantities do not need direction for their description.
- Scalar quantities are comparable only when they have the same physical dimensions.
- Two or more than two scalar quantities measured in the same system of units are equal if they have the same magnitude and sign.
Scalar quantities are denoted by letters in ordinary type.
- Scalar quantities are added, subtracted, multiplied or divided by the simple rules of algebra.
Work, energy, electric flux, volume, refractive index, time, speed, electric potential, potential difference, viscosity, density, power, mass, distance, temperature, electric charge etc. are examples of scalar quantities.
Properties of Vector Quantities:
Physical quantities having both magnitude and direction with appropriate unit are known as “VECTOR QUANTITIES”.
- We can’t specify a vector quantity without mention of direction.
- Vector quantities are expressed by using bold letters with arrow sign.
- Vector quantities can not be added, subtracted, multiplied or divided by the simple rules of algebra.
- Vector quantities added, subtracted, multiplied or divided by the rules of trigonometry and geometry.
Velocity, electric field intensity, acceleration, force, momentum, torque, displacement, electric current, weight, angular momentum etc are examples of vector quantities