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

If vec r=3vec p+4vec q and 2vec r=vec p-3vec q then

If vec p xxvec q=vec r and vec p*vec q=c, then vec q is

For three vectors vec p,vec q and vec r if vec r=3vec p+4vec q and 2vec r=vec p-3vec q then

If vec P and vec Q are two vectors, then the value of (vec P + vec Q) xx (vec P - vec Q) is

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 | =

If the vectors 3vec p+vec q;5p-3vec q and 2vec p+vec q;4vec p-2vec q are pairs of mutually perpendicular vectors, then find the angle between vectors vec p and vec q

Prove that [vec(p) - vec(q) vec(q) - vec(r) vec(r) - vec(p)] = 0

Find the angle between the vectors vec a = 2 vec p + 4 vec q and vec b = vec p- vec q where vec p and vec q are unit vectors forming an angle of 120^@ .