Transcription of VECTOR IDENTITIES AND THEOREMS
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VECTOR IDENTITIES AND THEOREMS
BVECTORIDENTITIESANDTHEOREMSA=X Ax+YAy+ZAzA+B=X(Ax+Bx)+Y(Ay+By)+Z (Az+Bz) +AyBy+AzBzAAAXYzAxB=detIAxAyAzBxByBz=X (AyBz-AzBy)+y(A~Bx-AxBz)+Z (AxBy-AyBx)A.(Bx C)=B. (CxA)= C.(AxB)Ax(Bx C)=(A. C)B-( )C(AxB). (CxD)=( )(B. D)-( )(B. C)V'x V'\I1=0V'. (V'xA)=0V'x(V'xA)=V'(V'.A)-V'2A----1--(V 'xA)xA=(A. V')A- -V'( )2V'(\11<1 =\11V'<I>+<I>V'\11V'. (\11A)=A. V'\I1+\I1V'. 'x('11A)=V"I1xA+ 'I1V'xAV'( )=( ')B+( ')A+Ax(V'xB)+Bx (V'xA)V'.(AxB)=B. (V'xA)-A. (V'xB)V'x(AxB)=A(V'.B)-B(V'.A)+(B. V')11- (:4. V')BGauss'sDivergenceTheorem:IvV'.Gdv= 'sTheorem:L(V'x G).it da= EXPLICITFORMSOFVECTOROPERATORSC artesian(x,y,z):Aa'l1Aa'l1Aa'l1V"I1=x-+y -+z-axayazAaAxaAyaAzV'.)
B VECTOR IDENTITIES AND THEOREMS A = X Ax + Y Ay + Z Az A + B = X (Ax + Bx) + Y (Ay + By) + Z (Az + Bz) A . B = AxBx + AyBy + AzBz A A A X Y z A x B = det IAx Ay Az Bx By Bz = X (AyBz - AzBy) + y (A~Bx - AxBz) + Z (AxBy - AyBx) A. (B x C) = B .(C x A) = C.(A x B)
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