If ABC is a triangle, then what is the value of the determinant

If $$\left|\begin{array}{ccc}1 & 1 & 0 \\x^2+2 x+2 & 1 & 0 \\2 & 1 & 1\end{array}\right|=0$$​, then the value of $$x$$​ is

​$$\text { The value of the determinant }\left|\begin{array}{lll}b^2-a b & b-c & b c-a c \\a b-a^2 & a-b & b^2-a b \\b c-a c & c-a & a b-a^2\end{array}\right|=\text { ? }$$​​

​$$\text { If }\left|\begin{array}{ccc}2 x-4 & 4 & 0 \\2 & x-1 & 1 \\2 & 2 & 0\end{array}\right|=0 \text {, then } x=\text {?}$$​​

The area of the triangle (in $$\text{unit}^2$$​) whose vertices are A(4, 8), B(-6, 2) and C(5, 4) is:

If in a triangle ABC, sin³A + sin³B + sin³C = 3 sinA sinB sinC, then what is the value of the determinant

are sides of the triangle?