Determinants Te...

If $$\displaystyle A= \begin{bmatrix}0 &i-\sin x  &i- \cos x\\sin x -i &0  &\sin x-i \\cos x-i &- \sin x+ i  &0 \end{bmatrix}$$ then $$\displaystyle \left | A \right |$$ equals

If every element of third order determinant of $$\displaystyle \Delta $$ is multiplied by 5 then value of new determinant equals to,

The points $$(a, b + c), (b, c + a)$$ and $$(c, a + b)$$ are

$$\displaystyle A=\begin{bmatrix}1 &-1  &1 \\2
 &1  &-3 \\1  &1  &1 \end{bmatrix}$$ and $$\displaystyle B= \begin{bmatrix}4 &2  &2 \\-5
 &0  &\alpha \\1  &-2  &3 \end{bmatrix}$$ If $$B$$ is the adjoint of $$A$$ then $$\displaystyle \alpha$$ equals

 If $$(-3, 11), (6, 2)$$ and $$($$$$k$$$$, 4)$$ are  collinear points, then $$k$$ is equal to

If the points $$\displaystyle \left(\frac{2}{5}, \frac{1}{3}\right), \left(\frac{1}{2} , k \right)$$ and $$\displaystyle \left(\frac{4}{5}, 0 \right)$$ are collinear then find the value of k

The points $$A(7, 8), B(-5, 2)$$ and $$ C(3, 6) $$ 

If $$\omega \neq 1$$ is a complex cube root of unity, and
$$x+iy=\begin{vmatrix}
1 & i & -\omega \\
-i & 1 & \omega ^{2}\\
\omega  & -\omega ^{2} & 1
\end{vmatrix}$$
then

If $$\displaystyle \Delta =\begin{vmatrix}
0 &b-a  &c-a \\
a-b &0  &c-b \\
a-c &b-c  &0
\end{vmatrix}$$ then $$\displaystyle \Delta $$ is equal to

If points $$(x,0)$$, $$(0,y)$$ and $$(1,1)$$ are collinear then the relation is-