Coordinate Geometry: JEE Main 2022 Mathematics question

The equations of the sides $\mathrm{AB}, \mathrm{BC}$ and $\mathrm{CA}$ of a triangle $\mathrm{ABC}$ are $2 x+y=0, x+\mathrm{p} y=15 \mathrm{a}$ and $x-y=3$ respectively. If its orthocentre is $(2, a),-\frac{1}{2}<\mathrm{a}<2$, then $\mathrm{p}$ is equal to ______________.