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

Explanation

`vecp,vecq,vecr`

`vecs=4vecp+3vecq+5vecr`

`vecs=x(-vecp+vecq+vecr)+y(vecp-vecq+vecr)+z(-vecp-vecq+vecr)`

`vecs=vecp(-x+y-z)+vecq(x-y-z)+vecr(x+y+z)`

`x+y+z=5-(1)`

`x-y-z=3-(2)`

`-x+y-z=4-(3)`

From equation 1 and 2

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