The vectors
`veca=xhati+(x+1)hatj+(x+2)hatk`,
`vecb=(x+3)hati+(x+4)hatj+(x+5)hatk`
and `vecc=(x+6)hati+(x+7)hatj+(x+8)hatk` are coplanar for

Options

A. all values of `x`
B. `x lt 0` only
C. `x gt0` only
D. None of these

Answer

A

Explanation

Vectors `veca, vecb, vecc` will be coplanar, iff
`[(veca, vecb, vecc)]=|(x,x+1,x+2),(x+3,x+4,x+5),(x+6,x+7,x+8)|`
`implies[(veca, vecb, vecc)]=|(x,x+1,x+2),(3,3,3),(6,6,6)|` [ Applying `R_(2)toR_(2)-R_(1),R_(3)toR_(3)-R_(1)`]
`implies[(veca, vecb, vecc)]=0` for all `x` [ `:' R_(1)` and `R_(2)` are proportional]
Hence vectors are coplanar for all values fo `x`