If \(\begin{vmatrix} -1 & a & a^2\\  -1 & b & b^2\\ -1 & c& c^2\\ \end{vmatrix}\) = λ and a - b = 1, b - c = 2 and c - a = 3, then the value if λ is

36

\(\begin{vmatrix} -1 & a & a^2\\  -1 & b & b^2\\ -1 & c& c^2\\ \end{vmatrix}=(-1)^2\begin{vmatrix} 1 & a & a^2\\  1 & b & b^2\\ 1 & c& c^2\\ \end{vmatrix}=λ\)

$= (a-b)^2(b-c)^2(c-a)^2=λ$

$=(1)^2(2)^2(3)^2=λ$

$=(1)(4)(9)=λ$

$=36$

Option 2nd is correct.