The value of determinant $\left|\begin{array}{lll}a-b & b+c & a \\ b-a & c+a & b \\ c-a & a+b & c\end{array}\right|$ is

If $\left(x_1, y_1\right),\left(x_2, y_2\right)$ and $\left(x_3, y_3\right)$ are the vertices of a triangle whose are is ' $k$ ' square units, then $\left|\begin{array}{lll}x_1 & y_1 & 4 \\ x_2 & y_2 & 4 \\ x_3 & y_3 & 4\end{array}\right|^2$ is

Let $A$ be a square matrix of order $3 \times 3$, then $|5 A|$ is equal to

$$ \text { } \begin{aligned} Let\,\,\,\Delta & =\left|\begin{array}{lll} A x & x^2 & 1 \\ B y & y^2 & 1 \\ C z & z^2 & 1 \end{array}\right| \text { and } \Delta_1 =\left|\begin{array}{ccc} A & B & C \\ x & y & z \\ z y & z x & x y \end{array}\right| \text {, then }\left|\begin{array}{ccc} A x & B y & C y \\ x^2 & y^2 & z^2 \\ 1 & 1 & 1 \end{array}\right| \end{aligned} $$