The two lines $lx + my = n$ and $l'x + m'y = n'$ are perpendicular if

The angle between the line $x+y=3$ and the line joining the points $(1,1)$ and $(-3,4)$ is

If the straight line $2x - 3y + 17 = 0$ is perpendicular to the line passing through the points $(7, 17)$ and $(15, \beta)$,then $\beta$ equals:

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is

If $\alpha, \beta$ $(\alpha > \beta)$ are two values of $k$ such that the equations $2x + (3 - 2k)y + (2k + 1) = 0$ and $kx + (k - 1)y - 4 = 0$ represent two perpendicular lines,then $\alpha^2 + 2\beta =$

If the line through the points $(-2, 6)$ and $(4, 8)$ is perpendicular to the line passing through the points $(8, 12)$ and $(x, 24)$,then the value of $x$ is