Question

Suppose that `vecp, vecq and vecr` are three non-coplanar vectors in `R^(3)`. Let the components of a vectors `vecs` along `vecp, vecq and vecr` be 4, 3 and 5, respectively. If the components of this 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

Answer 1

Correct Answer - 9
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`