Scalar and Vector Quantities

Scalar is a physical quantity that has magnitude but no direction. E.g. distance, mass, density, volume, time, speed, temperature, energy etc.

Vector is a physical quantity that has both magnitude and direction. E.g. displacement, velocity, acceleration, weight, force, momentum, force field etc.
Vector is represented with a straight line with arrow head pointing towards the direction of the vector and its length varying directly with the magnitude of the vector.

Resultant vector is a single vector which produces the same effect on an object as two or more vectors that is applied to the object. Addition of two or more vectors acting parallel, perpendicular or at an angle to one another is done using:

  1. Parallelogram law
  2. triangle law
  3. Pythagoras theorem

Parallelogram Law of vector states that if two vectors acting on a body are represented in magnitude and direction by the two adjacent sides of a parallelogram drawn from a point, their resultant vector is represented in magnitude and direction by the diagonal of the parallelogram drawn from the same point.

Vector Diagram Credit: Shutterstock

Triangle law of vector states that, if two vectors acting at a point are represented in magnitude and direction by the two adjacent sides of a triangle taken in order, the resultant vector is represented in magnitude and direction by the third side of the triangle taken in the reversed order.

The process of finding the components of vectors in a given direction is known as resolution of vector into its components. If a vector V is inclined at an angle Θ to a horizontal direction