The vectors `(a,a+1, a+2)(a+3, a+4, a+5)(a+6, a+7, a+8)` are coplanar for

Options

A. `AA a in R`
B. `AA a cancel in R`
C. `a = sqrt(-3)`
D. None of these

Answer

A

Explanation

Vectors `(a, a+1, a+2), (a+3, a+4,a+5) and (a+6, a+7,a+8) ` are coplanar.
`therefore |(a, a+1,a+2),(a+3, a+4, a+5), (a+6, a+7, a+8)|=0`
On applying `C_(2) to C_(2) - C_(1) and C_(3) to C_(1)`, we get
`|(a,1,2),(a+3,1,2),(a+6,1,2)|=0`
Hence, vectors are coplanar, `AA a in R`.