The value of $p$ such that the vector $\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ is an eigenvector of the matrix $\left[\begin{array}{ccc}4 & 1 & 2\\ p & 2 & 1\\ 14& -4& 10\end{array}\right]$ is:

The equation of the graph shown here is:

The solution of linear in equalities $x+y\ge 5$ and $x-y\le 3$ lies:

Find the ratio in which line $3x+2y=17$ divides the line segment joined by points $\left(2,5\right)$ and $\left(5,2\right).$

Find the area of the triangle formed with the three straight lines represented by:

$$\begin{gathered} \left(i\right) x+y=0 \\ \left(ii\right) 3x = 5y; and \\ \left(iii\right) y=3x-12 \end{gathered}$$