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 Multiplication of Vectors ( dot/scalar & cross/vector product ) d1 = |A| ; d2=|B| ; d3=|C| ; d4=|AxB| ;d5=|(AxB)xC| d6=A.(BxC) ; BxC = a61 i +a62 j +a63 k ; y= angle between A and B ; z1= cosine of angle between A and B angle η in degreeangle φ in degreecon 1:θ=η - φcon 2:θ=η + φcon 3:θ=-(η - φ)con 4:θ=-(η + φ)angle θ in degree 1 2 3 4 angleradian sine cos angles  in degree θ1θ2 θ3θ4 i,j,k=x,y,zHere [ (AB)i, (AB)j]=k*(AB)k firstenterk1 afterenteringa11,a12,a13,a13is recomputedsothat a11+a12+a13=0 afterenteringa21,a22,a23 a22,a23isrecomputed based on k1value givenK=2k1 k1 A+B+C= π;   A(°):-B(°): k1 Puta21valuebeforepressing calculate. (number) Squareroot inverseno. square A Enter a11 i Enter a12 j Enter a13 k Find d1 B Enter a21 i Enter a22 j Enter a23 k Find d2 C Enter a31 i Enter a32 j Enter a33 k Find d3 Dimension of Vector space of A B C Det R trR sum1strowsum2ndrow sum3rdrow area1starea2nd area3rd Calculation to make M=Ms a23a   a23b first enter values of A,B M f2 + f + =0 Ms +Ve + -Ve +, (+ /-) discriminant 4 * (ABdis1c2+ABdis2) (ABdis4c2+ABdis3) - - normalizedA  na11 i j k Find nd1 normalizedB  na21 i j k Find nd2 normalizedC  na31 i j k Find nd3 Reciprocal of A(rA) i + j + k Find rd1 Reciprocal of B(rB) i + j + k Find rd2 Reciprocal of C(rC) i + j + k Find rd3 normalizedrA  nra11 i + j + k Find nrd1 normalizedrB  nra21 i + j + k Find nrd2 normalizedrC  nra31 i + j + k Find nrd3 k11=a112/a122+a122/a112 k12=a122/a132+a132/a122 k13=a112/a132+a132/a112 k1=k11-k12-k13 rA.A Find FindAngle(rA,A) in ° yraa Find 1/( d1rd1) Find d1rd1 k21=a212/a222+a222/a212 k22=a222/a232+a232/a222 k23=a212/a232+a232/a212 k2=k21-k22-k23 rB.B Find FindAngle(rB,B) in ° yrbb Find 1/( d2rd2) Find d2rd2 k31=a312/a322+a322/a312 k32=a322/a332+a332/a322 k33=a312/a332+a332/a312 k3=k31-k32-k33 rC.C Find FindAngle(rC,C) in ° yrcc Find 1/( d3rd3) Find d3rd3 nk11=na112/na122+na122/na112 nk12=na122/na132+na132/na122 nk13=na112/na132+na132/na112 nk1=nk11-nk12-nk13 nrA.nA=1/(d1rd1) Find FindAngle(nrA,nA)in ° nyraa Find nd1nrd1 nk21=na212/na222+na222/na212 nk22=na222/na232+na232/na222 nk23=na212/na232+na232/na212 nk2=nk21-nk22-nk23 nrB.nB=1/(d2rd2) Find FindAngle(nrB,nB)in° nyrbb Find nd2nrd2 nk31=na312/na322+na322/na312 nk32=na322/na332+na332/na322 nk33=na312/na332+na332/na312 nk3=nk31-nk32-nk33 nrC.nC=1/(d3rd3) Find FindAngle(nrC,nC)in° nyrcc Find nd3nrd3 Put value of y1y1 should be less than or equal to Put value of f1 Find y2a Find y3a y12 +y2a2 +y3a2= If A=ai+ck, find inverse fill up only f1 Find y2b Find y3b y12 +y2b2 +y3b2= inverse of A :iA1 i j k norm inverse of A :iA2 i j k norm A x iA1 i j k norm A x iA2 i j k norm A.iA1 angle(A,iA1)in ° A.iA2 angle(A,iA2)in ° X1:X2: X3a+ X3b: i* ; X4 X5 X23s: X1s X43s X5s Find A.B angle(A,B) deg (AxB).C=[abc] cos(A,B) Find B.C angle(B,C) deg cos(B,C) Find C.A angle(C,A) deg cos(A,C) E.F Find angle(E,F) deg |E+F| |E-F| |E+F| - |E-F| 2√(|E||F|cos (E,F) AxB Find a41 i Find a42 j Find a43 k Find d4 (AxB)+xy i Find abz42 j Find abz43 k Find d4 (AxB)-xy i Findabz42a j Find abz43a k Find d4 Angle((AxB)+,(AxB)-) in° |AxB|2 |A.B|2 |A|2 +|B|2 |A.B|2+ |AxB|2 (|A||B|)2 (a/2)2(d2-e2-f2)  + (b/2)2(e2-d2-f2)  + (c/2)2(f2-d2-e2)  LHS : abde+bcef+acdf  RHS: [ABxy+ ,  ABz] = (AB)x -  (AB)y =*ABxy- [ABxy- ,  ABz] = (AB)x +  (AB)y [ABxy+,ABxy-] = *(AB)z [ (AB)x, (AB)y]= *(AB)z [ (AB)y, (AB)z]= *(AB)x [ (AB)z, (AB)x]= *(AB)y Put value for Z1:(any arbitrary value) M1=(a11a21+a12a22+a13a23)- Z12 U1=(a12a23-a13a22) / (a13a21-a11a23) T1=(a12a21-a11a22) / (a13a21-a11a23) MUT1a BA vector1 i j k Norm BA vector2 i j k Norm BA vector1.BC vector = BAvec1.(AxB) (see fig below)BA vector2.BC vector CA vector1 i j k Norm CA vector2 i j k Norm A.(AxB) AxBvectorisperpendiculartoplane containingbothA,B B.(AxB) (AxB)xC Find a51 i Find a52 j Find a53 k Find d5 D Find a71 i Find a72 j Find a73 k Find d7 E Find a81 i Find a82 j Find a83 k Find d8 (AxB)xC=D - E, a91 i Find a92 j Find a93 k F Find a101 i Find a102 j Find a103 k Find d10 Ax(BxC)=D - F, a111 i Find a112 j Find a113 k Find d11 (BxC) a121 i Find a122 j Find a123 k Ax(BxC)  a131 i Find a132 j Find a133 k A . ( BxC ) Find a61 i Find a62 j Find a63 k Find d6