上游究通大粤 SHANGHAI JLAO TONG UNTVERSITY Vector dot product: A·B=4B cos0 ii=j.j=k.k=1 ij=j.k=k.i=0
Vector dot product: A Bi = ABcosθ i.i = j.j = k.k =1 i.j = j.k = k.i = 0
上海文通大粤 SHANGHAI JIAO TONG UNIVERSITY commutative BxA=-AxB. A.B=B.A Distributive Ax(B+C)=AxB+AxC A.(B+C)=A.B+A.C Triple Product A.A A. A.(B×C)=B.(C×A)=C.(A×B)=BxB,B c,c,c Ax(B.C)=(A.C)B-(A.B)C (A×B)×C=(A.C)B-(B.C)A
commutative B× A = −A×B. A.B = B.A Distributive A× (B + C) = A× B + A×C A.(B + C) = A.B + A.C Triple Product Axyz A A ( )( )( ) ; BBB xyz CCC A. B C B. C A C. A B ×= ×= ×= Triple Product CCC x y z A B C A.C B A.B C ×( )( ) ( ) ( )( ) ( ) ⋅ = − ( ) ( )() × = A B C A.C B B.C A × ×= −
上海文通大 SHANGHAI JIAO TONG UNIVERSITY A A.(BxC)= BC 小码0 ECA 5G小 马G4 n G小码 =一 U U = C民A B A
上浒文通大学 SHANGHAI JIAO TONG UNIVERSITY Some useful trigonometric identities: ejote-io ,sin0=-j eioe-io 2 2 1-tan2(号) 2ian(号 c0s0=- ,sin= 1+tan2(号) 1+iam(? cos(0±)=cos(0)cos(p)干sin(O)sin(p) sin(0±)=sin(θ)cos(p)±cos()sin(p)
Some useful trigonometric identities: cos sin jj jj ee ee j θθ θθ θ θ − − + − 2 cos ,sin 2 2 1 () 2 () θ θ j θ θ = =− 2 2 2 1 tan () 2 tan( ) 2 2 cos ,sin 1t () 1t () θ θ θ θ θ θ − = = 2 2 1 tan () 1tan ( ) 2 2 cos( ) cos( )cos( ) sin( )sin( ) θφ θ φ θ φ + + ± = ∓ sin( ) sin( )cos( ) cos( )sin( ) θφ θ φ θ φ θ φ θ φ θφ ± = ±= ± ∓