If `vec(a),vec(b),vec(c)` are coplanar vectors, show that `(vec(a)xxvec(b))xx(vec(c)xxvec(d))=vec(0)`

If vec(a),vec(b),vec(c) are the non-coplanar vectors, then (vec(a).vec(b)xxvec(c))/(vec(c)xxvec(a).vec(b))+(vec(b).vec(a)xxvec(c))/(vec(c).vec(a)xxvec(b))= ……………

If vec(a),vec(b),vec(c) are three non-coplanar vectors such that vec(a)xx(vec(b)xxvec(c))=(b+c)/(sqrt(2)), then the angle between vec(a)andvec(b)" is "

Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxvec(b))xx(vec(c)xxvec(d))=vec(0)" Let "P_(1)andP_(2) be the planes determined by the pairs of vectors, vec(a),vec(b)andvec(c),vec(d) respectively. Then the angle between P_(1)andP_(2) is

If vec(a),vec(b),vec(c) are non-coplanar, non-zero vectors such that [vec(a),vec(b),vec(c)]=3,"then"{"["vec(a)xxvec(b),vec(b)xxvec(c),vec(c)xxvec(a)"]"}^(2) is equal to

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

If vec(a)xx(vec(b)xxvec(c))=(vec(a)xxvec(b))xxvec(c)," where "vec(a),vec(b)vec(c) are any three vectors such that vec(b)*vec(c)ne0andvec(a)*vec(b)ne0," then "vec(a)andvec(c)" are "

If vec(a)andvec(b) are two unit vectors, then the vectors (vec(a)+vec(b))xx(vec(a)xxvec(b)) is parallel to the vector

If [vec(a),vec(b),vec(c)]=1, then the value of (vec(a)*(vec(b)xxvec(c)))/((vec(c)xxvec(a))*vec(a))+(vec(b)*(vec(c)xxvec(a)))/((vec(a)xxvec(b))*vec(c))+(vec(c)(vec(a)xxvec(b)))/((vec(c)xxvec(b))*vec(a)) is