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

According to question `vecs = 4 vecp + 3vecq + 5 vecr and vecs = x( - vecp + vecq + vecr ) + y(vecp - vecq + vecr) + z( -vecp - vecq + vecr)`
` therefore -x +y -z =4" "` (1)
`" " x -y -z =3" "`(2)
`" "x+y+z=5" "` (3)
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`