Prove that `(vec B timesvec c)*[vec A times(vec B timesvec C)]=0`

Prove that: ( vec a- vec b)*{( vec b- vec c)xx(vec c- vec a)}"=0

If vec A, vec B and vec C are vectors such that |vec B|-|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

Prove that ( vec a- vec b)dot{( vec b- vec c)xx( vec c- vec a)}=0

If vec a+vec b+vec c=0 , prove that (vec a xx vec b)=(vec b xx vec c)=(vec c xx vec a)

Prove that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b) and interpret it geometrically.

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) times vec(b)=vec(c) and vec(b) times vec(c)=vec(a)," prove that "vec(a), vec(b), vec(c) are mutually perpendicular and abs(vec(b))=1 and abs(vec(c))=abs(vec(a)) .

If vec a , vec b , vec c are three non-coplanar vectors, prove that [ vec a+ vec b+ vec c vec a+ vec b vec a+ vec c]=-[ vec a vec b vec c]

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

The scalar vec Adot ( ( vec B+ vec C)xx( vec A+ vec B+ vec C)) equals a. 0 b. [ vec A vec B vec C]+[ vec B vec C vec A] c. [ vec A vec B vec C] d. none of these

Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, vec b, vec c]]dot