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

Answer

`(9)`

Explanation

(9) According to question `vecs=4vecp+3vecq+5vecr`
`and vecs=x(-vecp+vecq+vecr)+y(vecp-vecq+vecr)+z(-vecp-vecq+vecr)`
`therefore -x+y-z=4`
`x-y-z=3`
`x+y+z=5`
Adding (1) and (2) , we get
`z=-(7)/(2)`
Adding (2) and (3) , we get
`x=4`
Adding (1) and (3) , we get
`y=9//2`
`therefore 2x+y+z=2(4)+1=9`