Mathematics - Vector Question with Solution | TestHub

Let the position vectors of three vertices of a triangle be $4\vec{p}+\vec{q}-3\vec{r},-5\vec{p}+\vec{q}+2\vec{r}$ and $2\overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{q}}+2\overrightarrow{\mathrm{r}}$. If the position vectors of the orthocenter and the circumcenter of the triangle are $\frac{\vec{p}+\vec{q}+\vec{r}}{4}$ and $\alpha \vec{p}+\beta \vec{q}+\gamma \vec{r}$ respectively, then $\alpha +2\beta +5\gamma$ is equal to :