Title 1. Vector Theory.pdf ✅

55 EH EduHulk Download Free Study Material from EduHulk.com • Physical quantities: Scalar and vector • Vector and vector notation • Different types of vectors • Multiplication of vector by a real number • Vector addition • Vector subtraction • Resolution of a vector in a plane • Scalar and vector products of vectors Contents... VECTOR F Scalar : • 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. • For example : Mass, density, charge, current, temperature, distance, speed etc. F Vector : • Any physical quantity which have magnitude as well as direction, and also follows laws of vector, are called vectors. • For example : velocity, displacement, force, acceleration, current density etc. • Vectors can be of two types : (i) Polar vector : These vectors have a starting point or a point of application. Example : Displacement. (ii) Axial vectors : These vector have direction along the axis of rotation. Ex : Angular velocity, angular momentum, torque, small angular displacement etc. à Note : Three conditions for physical quantity to be vector are - (i) It must have direction. (ii) It must follow vector addition law. (iii) It must follow commutative law in addition. F Vector Representation (Notation) : 1) Symbolic representation :- A single letter or double letter with an arrow overhead. Like we will represent force vector by  F . Its magnitude will be represented by F or  F


58 EH EduHulk Download Free Study Material from EduHulk.com • Vector Addition by Analytical Method : R P Q = + R = magnitude of resultant NB = Q sin ; ON = P + Q cos R 2 = (NB)2 + (ON)2 R = P Q PQ 2 2   2 cos  • Angle between resultant and vector are : tan  = NB ON Q P Q   sin cos   ; tan  = P Q P sin cos    Case - I :  = 0° R = P Q PQ 2 2    2 0 cos = P + Q  | | | | | | max    R P Q   Case - II :  = 180° R = P Q PQ 2 2    2 180 cos = P – Q or Q – P  | |min  R P Q   Case - III :  = 90° R = P Q PQ P Q 2 2 2 2      2 90 cos and tan  = Q P Case - IV : If P = Q  R P  2 2 cos  (i)  = 60°  R P  3 (ii)  = 90°  R P  2 (iii)  = 120°  R P  à Note : (i) |P – Q|  R  P + Q (Range) (ii) Direction of resultant is always closer to larger vector. (iii) Resultant of two vectors of unequal mangitude can never be zero. (iv) If vectors are of unequal magnitude then minumum three coplanar vectors are required for zero resultant. (v) If resultant of two unit vectors is another unit vector then angle between them () = 120o 3) Polygon law of vector addition :- If any number of vectors are represented by the sides of an open polygon taken in same order then their resultant is represented by the closing side of the polygon taken in reverse order. A  B C D  R