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))`

If vec(d)=vec(a)xx(vec(b)xxvec(c))+vec(b)xx(vec(c)xxvec(a))+vec(c)xx(vec(a)xxvec(b))," then "

Prove that [vec(a)+vec(b)+vec(c),vec(b)+vec(c),vec(c)]=[vec(a)vec(b)vec(c)]

For any three vectors vec(a),vec(b)andvec(c),(vec(a)+vec(b)).(vec(b)+vec(c))xx(vec(c)+vec(a)) is

Prove that (vec(a). (vec(b) xx vec(c)) vec(a) = (vec(a) xx vec(b)) xx (vec(a) xx (c)) .

If the volume of the parallelpiped with vec(a)xxvec(b),vec(b)xxvec(c),vec(c)xxvec(c)xxvec(a) as coterminous edges is 8 cubic units, then the volume of the parallelepiped with (vec(a)xxvec(b))xx(vec(b)xxvec(c)),(vec(b)xxvec(c))xx(vec(c)xxvec(a))and(vec(c)xxvec(a))xx(vec(a)xxvec(b)) as coterminous edges is,

Let vec(a),vec(b)andvec(c) be three non-coplanar vectors and let vec(p),vec(q),vec(r) be the vectors defined by the relations vec(p)=(vec(b)xxvec(c))/([vec(a)vec(b)vec(c)]),vec(q)=(vec(c)xxvec(a))/([vec(a)vec(b)vec(c)]),vec(r)=(vec(a)xxvec(b))/([vec(a)vec(b)vec(c)])" Then the value of "(vec(a)+vec(b))*vec(p)+(vec(b)+vec(c))*vec(q)+(vec(c)+vec(a))*vec(r)=

If vec(a)+vec(b)+vec(c)=0," then show that "vec(a)xxvec(b)=vec(b)xxvec(c)=vec(c)xxvec(a)

For any non-zero vectors vec(a)andvec(b)vec(a)xxvec(b) is