If the image of the point P (1,2, a) in the line (x-6)/3=(y-7)/2=(7- z)/2 is Q (5, b, c ), then a^2+b^2+c^2 is equal to

If the image of the point $\displaystyle \mathrm{P}(1,2, a)$ in the line $\displaystyle \frac{x-6}{3}=\frac{y-7}{2}=\frac{7-\mathrm{z}}{2}$ is $\displaystyle \mathrm{Q}(5, b, \mathrm{c})$, then $\displaystyle a^2+b^2+c^2$ is equal to