Tiêu đề 03_VIII_OLY._PHY._VOL-1_WS-3-4 & KEY(VECTORS)_25 to 55.pdf ✅

VIII - PHYSICS (Vol-1) Olympiad Text Book Narayana Group of Schools 27 Direction of the resultant : The resultant makes angle ‘ ’ with A  (say) From triangle CAE : EC EC tan AE AB BE     Qsin tan P Qcos       1 Qsin tan P Qcos               (4) The expression (3) and (4)gives the magnitude and direction of the resultant of P  and Q  . SPECIAL CASES:1) If P  and Q  are in same direction, then    0 , and cos  = 1  From equation (3) and (4), R P Q      and  = 0 Hence the magnitude of resultant is sum of the magnitude of individual vectors. The direction of resultant is same as that of individual vectors. 2)If P  and Q  are opposite, then  = 180° and cos  = –1  R P Q      i.e., R P Q      or Q P   and    0 or 180°. Thus the magnitude of resultant is equal to difference of magnitudes of individual vectors and the direction of resultant is same as that of the vector of larger magnitude. 3) If P  and Q  are perpendicular, then    90 & cos  = 0  R 2 2   P Q and  = Tan–1 (Q/P) 4) If P Q    , then R = 2P cos  /2 and   /2  If the vectors have equal magnitude, then the resultant will bisect the angle between them. Example for a parallelogram law of vectors: A current in a wire is represented by the direction but it is not vector quantity because it does not obey the laws of vector addition. In figure the current flowing in wire OC = current in wire AO + current in wire BO i i1 i2 A B C O  i i1 i2 A B C O  i = i1 +i2 If the current is a vector then i will be i = 2 2 1 2 1 2 i i 2i i cos    according to parallelogram law of vector addition.