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    y) ~LLI. VECTORS  Pre-Medical :  Physics   Scalar Quantities A physical quantity which can be described completely by its magnitude only and does not require a direction is known as a scalar quantity. . It obeys the ordinary rules of algebra. Ex: Distance, mass, time, speed, density, volume, temperature, electric current etc. Vector Quantities A physical quantity which requires magnitude and a particular direction, when it is expressed. Ex.: Displacement, velocity, acceleration, force etc. A vector is represented by a line headed with an arrow. Its length is proportional to its magnitude.  A is a vector.  A=PQ Magnitude of  A = IAI or A .1Types of vector ·1 Parallel Vectors :- Those vectors which have same direction are called parallel vectors. Angle  between two parallel vectors is always 0° ã ..ã. B   ã ã Equal Vectors Vectors which have equal magnitude and same direction are called equal vectors. ã  Anti-parallel Vectors : Those vectors which have opposite direction are called anti-parallel vector. Angle  between two anti-parallel vectors is always 180°  ' Of >' >;- 0 :: iE ;<!' :I: ~ \,I ~ § ~I :5 ~ ~ 13 ~ ~ 3 N E ã Negative (or Opposite) Vectors Vectors which have equal magnitude but opposite direction are called negative vectors of each other. AB and BA are negative vectors  A------- ãã B AB=-BA  A ...ããã ---------B ã  Co-initial vector Co-initial vectors are those vectors which have the same initial point. In figure ii, band c are co-initial vectors. ~ ..ã. a ã  Collinear Vectors: The vectors lying in the same line are known as collinear vectors. Angle between collinear vectors is either 0° or 180°.   ã  17 ã -  ..,LIM------------ Examp,le. +-- +-- (8 = 0°) +-- --+ (8 = 180°) (ii) (iv) --+ --+ (8 = 0°) --+ +-- (8 = 180°) ã    Coplanar Vectors Vectors located in the same plane are called coplanar vectors. Note:- Two vectors are always coplanar. ã  Concurrent vectors \y'  /' Those vectors which pass through a common point are called concurrent vectors In figure ii, band c are concurrent vectors. ·2 Null or Zero Vector A vector having zero magnitude is called null vector. Note: Sum of two vectors is always a vector so, (A) + (-A) = 6 6 is a zero vector or null vector. ·3 Unit Vector A vector having unit magnitude is called unit vector. It is used to specify direction. A unit vector is represented  by  A (Read as A cap or A hat or A caret). Unit vector in the direction of  A is unit vector» __________V_e_c_to_r ____  l Magnitude of the vector) Base Vectors In an XYZ co-ordinate frame there are three unit vectors i ,  j and k, these are used to indicate X, Y and Z directions respectively. These three unit vectors are mutually perpendicular to each other. ·4 Polar Vector Vectors which have initial point or a point of application are called polar vectors. Ex.: Displacement, force etc. ·5 Axial Vector These vectors are used in rotational motion to define rotational effects. Direction of these vectors is always along the axis of rotation in a.ccordance with right hand screw rule or right hand thumb rule. Ex.: Infinitesimal angular displacement (d8), Angular velocity (ill), Angular momentum (J), Angular acceleration (li) and Torque en 18    ã ã y (
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