Suppose that `vec p,vecqand vecr` are three non- coplaner in `R^(3)` ,Let the components of a vector`vecs` along `vecp , vec q and vecr` be 4,3, and 5, respectively , if the components this vector `vec s` along `(-vecp+vec q +vecr),(vecp-vecq+vecr) and (-vecp-vecq+vecr)` are x, y and z , respectively , then the value of `2x+y+z` is

Suppose that vecp, vecq and vecr are three non-coplanar vectors in R^3 . Let the components of a vector vecs along vecp, vecq and vecr be 4,3 and 5 respectively. If the componenets of ths vector vecs along (-vecp+vecq+vecr), (vecp-vecq+vecr) and (-vecp-vecq+vecr) are x, y and z respectively, then the value of 2x+y+z is.

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 three points (2 vecp-vecq+3 vecr),(vecp-2 vecq+alpha vecr) and (beta vecp-5 vecq) (where vecp, barq, vecr are non-coplanar vectors) are collinear, then the value of 1/(alpha+beta) is

If vecP -vecQ - vecR=0 and the magnitudes of vecP, vecQ and vecR are 5 , 4 and 3 units respectively, the angle between vecP and vecR is

If vecpxxvecq=vecr and vecp.vecq=c , then vecq is

If vecpxxvecq=vecr and vecp.vecq=c , then vecq is

If vecp,vecq and vecr are perpendicular to vecq + vecr , vec r + vecp and vecp + vecq respectively and if |vecp +vecq| = 6, |vecq + vecr| = 4sqrt3 and |vecr +vecp| = 4 then |vecp + vecq + vecr| is