#### IIT (NTSE/Olympiad)

# Vector

__Vector__

__Vector__

**1. VECTOR**

**(a)**The physical quantities which have magnitude and direction and which can be added according to the triangle rule, are called vector quantities. Examples : force, linear momentum, electric field, magnetic field etc.

**(b)**If a physical quantity has magnitude as well as direction but does not add up according to the triangle rule, it will not be called a vector quantity. Example Electric current in a wire has both magnitude and direction but there is no any meaning of triangle rule. Thus, electric current is not a vector quantity.

**1.1 Various types of vectors.**

**(a) Polar Vectors :**

Vectors having starting point (as in case of displacement) or point of application (as in case of force) are polar vectors.

**(b) Axial vectors**

Vectors representing rotational effects and are always along the axis of rotation in accordance with right hand screw rule are axial vectors.

**Ex.**Angular displacement (θ); Angular velocity (ω) ; Angular acceleration (α) ; Torque (τ) etc.

**1.2 Some other types of vectors :**

**(a) Zero vector :**

A vector with zero magnitude is called zero vector.

**(b) Proper vector :**

A vector with non-zero magnitude is called proper vector.

**(c) Like vectors:**

Two (or more) vector are called like vectors if their supports are same or parallel and are in the same sense.

**(d) Unlike vectors :**

Two vectors are called unlike vectors if their supports are same or parallel and are in the opposite sense.

**(e) Equal vectors :**

Two vectors are called equal (or equivalent) vectors if they have equal magnitude, same or parallel supports and same sense.

**(f) Collinear vectors :**

Two (or more) vectors are called collinear vectors if they have same or parallel supports.

**(g) Coplanar vectors :**

Three (or more) vectors are called coplanar vectors if they lie in the same plane or are parallel to the same plane. Two (free) vectors are always coplanar.

**(h) Negative vector :**

A vector having the same magnitude as that of the given vector but directed in the opposite sense is called the negative of the given vector.

**(i) Unit vector :**

A vector with magnitude of unity is called unit vector. Unit vector in the direction of a is = a/|a|

#### IIT (Class X)

- Unit, Dimension & Error

- Vectors

- Motion in One Dimension

- PROJECTILE MOTION

- NEWTON'S LAWS OF MOTION & FRICTION

- WORK, POWER, ENERGY & CONSERVATION LAWS

- CIRCULAR MOTION & ROTATIONAL DYNAMICS

- GRAVITATION