向量与数的乘法

( 英 文 ) V ectors may also be m ult ip lied by a number．T he produ ct of th e vec tor a by t he n umb er is defined as t he vector a 一 a ， th e absolute value of w hic h is obtained by m ultiply ing t he absolute value of t he vec tor口 by t he absol ute valu e of the number ，i．e．( a (== ( ( {a (，the direction coinciding with t he direct ion of t he vec tor a or being in t he oppos ite sense dependin g on whet her >0 or <二0 ． If 一 0 or a = 0 ．t hen a is consid ered t o be eq ual t o t he zero vect or． T h e m ult iplicat ion o f a vec to r b y a n u mb er p os sess es th e ass ociativ e Iaw and t w o d ist rib ut ive Iaw s．N amely ．fo r any nu mb er s ， and vecto rs a ，b ( 口) ： ( ) 口( ass oc iat ive 1aw ) ． +． 、。 。． 。I(distrib ti、，e· (a+ )===入口+ b f u Ve laws)． L et us pro ve t h ese p rop er ties． T h e abso lu te val ues of t he vec to rs ( a ) an d ( ) a are the same and are equal to f f f f f口f．The directions of th ese vect or s eit her co incid e w it h t he d irect ion o f th e vect or a ，if a nd are of t he same sig n ，or being in t h e op pos it e s ens e， if an d h ave dif fer en t sig n s． H en ce ，t h e vect ors ( 口) a nd ( ) a are eq ual by ab so lu te val ue an d are i n t h e sam e direct ion ，consequ ent ly ，t h ey are equa 1． I f at 1east o ne of t h e num b ers ， ’，or t h e vector a is equ al to zero ，th en bo t h vec to rs are equa 1 to zero an d ，h en ce ，t h ev are eq ual to each ot h er．T he as so ciativ e Iaw is t h us p rov ed． W e are no w go ing t o...