# Bernoulli’s Theorem & its application

## Introduction of Vector

Physical quantities having magnitudedirection and obeying laws of
vector algebra
are called vectors.
Example : Displacement, velocity, acceleration, momentum, force,
impulse, weight, thrust, torque, angular momentum, angular velocity etc.
Note : If a physical quantity has magnitude and direction both, then it does not always imply that it is a vector. For it to be a vector the third condition of obeying laws of vector algebra has to be satisfied.
Example : The physical quantity current has both magnitude and
direction but is still a scalar as it disobeys the laws of vector algebra.

## Types of Vector

(1) Equal vectors : Two vectors A and B
are said to be equal when they
have equal magnitudes and same direction.

(2) Parallel vector : Two vectors A and B are said to be parallel
when
(i) Both have same direction.
(ii) One vector is scalar (positive) non-zero multiple of another
vector.

(3) Anti-parallel vectors : Two vectors A and B are said to be anti-parallel when
(i) Both have opposite direction.
(ii) One vector is scalar non-zero negative multiple of another
vector.

(4) Collinear vectors : When the vectors under consideration can
share the same support or have a common support then the considered vectors are collinear.

(5) Zero vector (0): A vector having zero magnitude and arbitrary
direction (not known to us) is a zero vector.

(6) Unit vector : A vector divided by its magnitude is a unit vector.

(7) Polar vectors : These have starting point or point of application .
Example displacement and force etc.

(8) Axial Vectors : These represent rotational effects and are always
along the axis of rotation in accordance with right hand screw rule. Angular velocity, torque and angular momentum, etc., are example of physical quantities of this type.

(9) Coplanar vector : Three (or more) vectors are called coplanar vector if they lie in the same plane. Two (free) vectors are always
coplanar.