Components and addition of vectors in 2D and 3DHard

Orthocenter and Circumcenter Relations

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 $2\vec p - \vec q + 2\vec r$ . 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 :

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