SOLUTION: If vector x is denoted by V(x), If v(d)=p(V(a)XV(b))+q(V(b)XV(c))+r(V(c)XV(a)) and [V(a),V(b),V(c)]=1/8 then p+q+r is equal to A.8V(d)(V(a)+V(b)+V(c)) B.4V(d)(V(a)+V(b)+V(c))

Algebra ->  Vectors -> SOLUTION: If vector x is denoted by V(x), If v(d)=p(V(a)XV(b))+q(V(b)XV(c))+r(V(c)XV(a)) and [V(a),V(b),V(c)]=1/8 then p+q+r is equal to A.8V(d)(V(a)+V(b)+V(c)) B.4V(d)(V(a)+V(b)+V(c))       Log On


   

Question 31495: If vector x is denoted by V(x),
If v(d)=p(V(a)XV(b))+q(V(b)XV(c))+r(V(c)XV(a)) and [V(a),V(b),V(c)]=1/8 then
p+q+r is equal to
A.8V(d)(V(a)+V(b)+V(c))
B.4V(d)(V(a)+V(b)+V(c))
C.8V(d)
D.(V(a)+V(b)+V(c))V(d)
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
FOR EASE OF TYPING LET US DENOTE VECTORS V(a)ETC...BY A AND SCALARS P,Q,R BY p,q,r.
WE ARE GIVEN
D=p(AXB)+q(BXC)+r(CXA)............AND (A,B,C)=1/8
DOT BOTH SIDES WITH C
D.C=p(A,B,C)+q(B,C,C)+r(C,A,C)=p/8
p=8(D.C)......SIMLARLY....q=8(D.A).............r=8(D.B)
HENCE...p+q+r=8{(D.C)+(D.A)+(D.B)}=8(D).(A+B+C)......
SO A IS THE ANSWER.