Determinants Te...

Let $$A$$ be a square matrix of order $$3\times 3$$ then $$\left| KA \right| $$ is equal to

Find the equation of line joining $$(1,2)$$ and $$(3,6)$$ using determinants. Let $$p(x,y)$$ be any point on the line joining $$(1,2)(3,6)$$

Value of determinant $$\begin{vmatrix} \cos 80^\circ & -\cos 10^\circ\\ \sin 80^\circ & \sin 10^\circ \end{vmatrix}$$ is:

Find the equation of the line joining $$(3,1)$$ and $$(9,3)$$ using determinants.

Value of determinant $$\begin{vmatrix} \cos 50^\circ & \sin 10^\circ\\ \sin 50^\circ & \cos 10^\circ \end{vmatrix}$$ is:

Co-factors of the first column of determinant
$$\begin{vmatrix} 5 & 20 \\ 3 & -1\end{vmatrix}$$

If $$a, b, c$$ are the $$p^{th}, q^{th}$$ and $$r^{th}$$ terms of an $${H}.{P}$$, then the lines $$bcx+py+1=0,\ cax+ qy+1=0$$ and $$abx+ry+1=0$$,

If $$x_{1},y_{1}$$ are the roots of $$x^{2}+8x-20=0$$ and  $$x_{2},y_{2}$$ are the roots of $$4x^{2}+32x-57=0$$ and $$x_{3},y_{3}$$ are the roots of $$9x^{2}+72x-112=0$$ such that $$y_{i}<0,$$ then the points $$(x_{1},y_{1}),(x_{2},y_{2})$$ and $$(x_{3},y_{3})$$

If the lines $$\mathrm{x}+\mathrm{p}\mathrm{y}+\mathrm{p}=0,\ \mathrm{q}\mathrm{x}+\mathrm{y}+\mathrm{q}=0$$ and $$\mathrm{r}\mathrm{x}+\mathrm{r}\mathrm{y}+1 =0 (\mathrm{p},\mathrm{q}, \mathrm{r}$$ being distinct and $$ \neq$$ 1) are concurrent, then the value of
$$\displaystyle \frac{p}{p-1}+\frac{q}{q-1}+\frac{r}{r-1}=$$

The coordinates of the point $$P$$ on the line $$2x+3y+1=0$$ such that $$|PA-PB|$$ is maximum, where $$A(2, 0)$$ and $$B(0, 2)$$ is