If `[(bara, barb, barc)]=2` and `(veca.vecb)=2, (vecc.veca)=5` then, `veca` is equal to `xbarb+ybarc+z(barbxxbarc)` (where `barb` & `barc` are two non -coplanar orthogonal unit vectors then`(x+y-z)=?`

Answer

5

Explanation

Let `bara=xbarb+ybarc+z(barbxxbarc)`
`impliesbara.barb=x(barb.bar)+y(barb.barc)=2`
`x+y(barb.barc)=2`…….(1)
`bara.barc=0+yxx1=5`
`y=5`
`bara.(barbxxbarc)=0+0+z|barbxxbarc|^(2)`
`z=2`