If `vec a,vec b,vec c` are three non-coplanar vectors represented by concurrent edges of a parallelopiped of volume 4, `(vec a+vec b)+(vec bxx vec c)+(vec b+vec c).(vec c xx vec a) + (vec c +vec a).(vec axx vec b)` is equal to

If vec(a),vec(b),vec(c) are three non-coplanar vectors represented by concurrent edges of a parallelepiped of volume 4 cubic units, find the value of (vec(a)+vec(b))*(vec(b)xxvec(c))+(vec(b)+vec(c))*(vec(c)xxvec(a))+(vec(c)+vec(a))*(vec(a)xxvec(b))

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

Let vec a , vec ba n d vec c be three non-coplanar vecrors and vec r be any arbitrary vector. Then ( vec axx vec b)xx( vec rxx vec c)+( vec bxx vec c)xx( vec rxx vec a)+( vec cxx vec a)xx( vec rxx vec b) is always equal to [ vec a vec b vec c] vec r b. 2[ vec a vec b vec c] vec r c. 3[ vec a vec b vec c] vec r d. none of these

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

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

For any three vectors vec a, vec b, vec c, (vec a-vec b) * (vec b-vec c) xx (vec c-vec a) is equal to

If vec a,vec b, and vec c are three non-coplanar vectors,then find the value of (vec a*(vec b xxvec c))/(vec b*(vec c xxvec a))+(vec b*(vec c xxvec a))/(vec c*(vec a xxvec b))+(vec c*(vec b xxvec a))/(vec a xxvec c))

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