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

If $\mathrm{O}(0,0), \mathrm{A}(1,2)$ and $\mathrm{B}(3,4)$ are the vertices of triangle OAB , then the joint equation of the altitude and median drawn from O is

The combined equation of two lines through the origin and making an angle of $45^{\circ}$ with the line $3 x+y=0$, is

The acute angle between the lines $x \cos 30^{\circ}+y \sin 30^{\circ}=3$ and $x \cos 60^{\circ}+y \sin 60^{\circ}=5$ is