If p,q and r are non-zero, non-coplanar vectors then [p+q-r p-q q-r]= . . .

If a,b,c are three non-coplanar vector, then the vectors equation r = (1 -p-q) a +p b +qc respesents a

If vec p + vec q + vec r = xvec s and vec q + vec r + vec s = yvec p and are vec p, vec q, vec r non coplaner vectors then | vec p + vec q + vec r + vec r + vec s | =

Suppose that vec p, vec q and vec r are three non-coplanar vectors in R^3. Let the components of a vector vec s along vec p, vec q and vec r be 4, 3 and 5, respectively. If the components of this vector vec s along (-vec p+vec q +vec r), (vec p-vec q+vec r) and (-vec p-vec q+vec r) are x, y and z, respectively, then the value of 2vec x+vec y+vec z is

Suppose that vec(p), vec(q) and vec(r) are three non-coplanar vectors in R. Let the components of a vector vec(s) along vec(p), vec(q) and vec(r) be 4, 3 and 5 respectively. If the components of this vector vec(s) " along" (-vec(p) + vec(q) + vec(r)), (vec(p) - vec(q) + vec(r)) and (-vec(p) - vec(q) + vec(r)) are x,y and z respectively, then the value of 2x + y + z is