Vectors are pairs consisting of a direction and magnitude that are usually represented by arrows. Vectors have basic properties including equality if they have the same magnitude and direction, and vectors can be opposite, parallel, or antiparallel based on their direction and magnitude. Components of a vector are obtained by subtracting the coordinates of the initial point from the terminal point, and vectors can be added, subtracted, and multiplied.

1. Introduction to Vectors
By: Dheeraj Pandey

2. Vectors
• Vectors are pairs of a direction and a
magnitude. We usually represent a vector
with an arrow:
• The direction of the arrow is the direction
of the vector, the length is the magnitude.

3. Basic Properties
1. Equality:
Two vectors are said to be equal if they
have the same magnitude and direction.
2. Opposite,Parallel or Antiparallel vector:
Two vectors are opposite if they have the same
magnitude but opposite direction.
Two vectors are parallel if they have the same
direction but not necessarily the same
magnitude.
Antiparallel if they have opposite direction but not
necessarily the same magnitude.

4. Components
• The initial point is the tail, the head is the
terminal point. The components are
obtained by subtracting coordinates of the
initial point from those of the terminal
point. v
(2,2)
(5,6)

6. Addition and Subtraction of
Vectors

7. Vector Multiplication

8. Applications