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 "`

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)andvec(b) are unit vectors such that [vec(a),vec(b),vec(a)xxvec(b)]=(pi)/(4)," then the angle between "vec(a)andvec(b)" is "

vec(a),vec(b)andvec(c) are said to be colpanar if

If |vec(a)xxvec(b)|=vec(a).vec(b), then angle between the vector vec(a)andvec(b) is ……………..

Let vec(a),vec(b),andvec(c) be three vectors having magnitudes 1,1,2 respectively. If vec(a)xx(vec(a)xxvec(c))+vec(b)=0, then the acute angle between vec(a)andvec(c) is ……………

Let veca,vecb,vecc be three non-zero vectors such that vec(c) is a unit vector perpendicular to both vec(a)andvec(c). If the angle between vec(a)andvec(c)" is "(pi)/(6)," show that "[vec(a),vec(b),vec(c)]^(2)=(1)/(4)absvec(a)^(2)absvec(b)^(2).

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 mutually perpendicular unit vectors,then |vec(a)+vec(b)+vec(c)| 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