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ZERO UNIT EQUAL COLLINEAR COPLANER VECTOR VECTOR VECTORS VECTORS VECTORS is unit vector |/@ & Bare equal : vector parallel eaannes oa tab ae pa iff vectors if || collines vector toor fil =|b]; waiet lying on the gb-b i [rane same plane. ' ~~ pif H External division Position Vector ; Internal Section 7 —rengeemegemeaty | oy Postition Vector of pt. Pis it. ieyit ak | | (na)+(mb) eer Vector joining two points A & B Rll) aa | External Section i. (mb)-(na): e——— | sm-nz0 AB= OB-OA = (2— xa )i+ (y2— yn )j + (22- 11k Part Il VECTOR LINES Lines : For a Vector equation of a line one needs => A Point online, let a. = A Parallel vector to the line, let b. xX ALLULLLLELELUELELLLLLLEALULALLELELELCLULENPUCLELULLELELELEELLLLLLSELEAMELLELEL EEE HM Parallel to b & Passes Through Point A | When Two Po on Line are Known —— cquition tthe une oc EERE | LUVLELELTELETTELTLTSTULETPETTLLTTLL TL LEE LLTNE EDEL LET ETEETEL PTTL LETT ELE LETTE L TELE TL EY | Shortest distance is measure along their | Cor A ‘common normal — Line Li & Lz will be coplaner — Required Condition ortest distance P; P2 = Ape) (ase Ext) a0 =ail LLL LL LLL Lhd hadddcdddddddddidiiéd; Scalar or Dot Product Vector or Cross Product 1 ‘+ TTA b+ ad's ask - A A Babil+by+ bk | 4 TS o | |! axb=|ai Cia by ra | ® Direction of resultant ® Dot product of aandb vector can be found is the projection of a over b. using Right Hand Rule MULLLLALALALALLULLLLLALALLLALLLULULLLLLADRLLLLLLLLALL ALLELE Scalar Triple Product Vector Triple Product (Bxe) > Be, Fx(Bxel H 1 ’ ' 4 1 SCALAR TRIPLE PRODUCT F(Bxe)=(aB ce] Fsahsag+ak - B= bil + ba} + bak t= aleal+ ak i(i) (axb).(exd)=a.bx(exd) | saf(b.d)c-(b.c)d}) = (a .<)(6 .d) - (a 4) (6) ) NOTE li) (axb)(exd)=[acd]b-[bed] (i) a’, bY & Care Coplanar iff (IBIE=O H Or=[ab d]c-[abc] oS 
