Solve the vector equation `vec r xx vec a + k vec r = vec b` , where `vec a, vec b` are two non-collinear vectors and k is any scalar.

solve the vector equation vec r xxvec a+kvec r=vec b, where vec a,vec b are two non-collinear vectors and k is any scaler.

If vec r* vec a =0 = vec r* vec b ,where vec a and vec b are non-coplanar vectors then

Solve the following equation for the vector vec p; vec p xx vec a+(vec p. vec b)vec c=vec b xx vec c where vec a ,vec b,vec c are non zero non coplanar vectors and vec a is neither perpendicular to vec b non to vec c hence show that (vec p xx vec a+([vec a vec b vec c])/(vec a*vec c) vec c) is perpendicular vec b-vec c.

Prove the following : vec a * (vec a xx vec b) = 0 , where are vec a and vec b are any two vectors.

If vec a xxvec b=vec b xxvec c!=0, where vec a,vec b and vec c are coplanar vectors,then for some scalar k

Are three points with position vectors vec a + vec b, vec a - vec b and vec a tau + vec b are collinear for all tau in R ? Give reasons.

If vec(a) xx vec(b) = vec(b) xx vec(c )= vec(c )xx vec(a) , where vec(a), vec(b), vec(c ) are non zero vectors, then

If vec r satisfies vec r xx (vec i + 2vec j + vec k) = vec i-vec k then for any scalar t, vec r =

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot