Let ` vec a , vec b ,a n d vec c` be non-coplanar unit vectors, equally inclined to one another at an angle`theta` . If ` vec axx vec b+ vec bxx vec c=p vec a+q vec b+r vec c ,` find scalars `p ,qa n dr` in terms of `thetadot`

Let vec a,vec b, and vec c be non-coplanar unit vectors,equally inclined to one another at an angle theta. If vec a xxvec b+vec b xxvec c=pvec a+qvec b+rvec c, find scalars p,q and r in terms of theta .

If vec a,vec b and vec c are three non-coplanar unit vectors each inclined with other at an angle of 30^(@), then the volume of tetrahedron whose edges are vec a,vec b,vec c is (in cubic units)

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

For any three vectors adotb\ a n d\ c write the value of vec axx( vec b+ vec c)+ vec bxx( vec c+ vec a)+ vec cxx( vec a+ vec b)dot

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to

If vec a, vec b, vec c are three non-coplanar vectors such that vec a + vec b + vec c = alphavec d and vec b + vec c + vec d = betavec a then vec a + vec b + vec c + vec d is equal to

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0 then vec r is equal to

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0, then vec r is equal to