If the mirror image of the point (2,4,7) in the plane $3x-y+4z=2$ is (a, b, c), then $2a+b+2c$ is equal to :

The equation of plane is 3x – y + 4z = 2
the mirror image of point (2,4,7) in given plane is (a, b, c) then
$\begin{array}{l}\frac{\mathrm{a}-2}{3}=\frac{\mathrm{b}-4}{-1}=\frac{\mathrm{c}-7}{4}=-\frac{2(6-4+28-2)}{(9+1+16)}\\ \frac{\mathrm{a}-2}{3}=\frac{\mathrm{b}-4}{-1}=\frac{\mathrm{c}-7}{4}=-\frac{28}{13}\\ \frac{\mathrm{a}-2}{3}=-\frac{28}{13}\Rightarrow \mathrm{a}=\frac{-28\times 3}{13}+2=\frac{-58}{13}\\ \frac{\mathrm{b}-4}{-1}=\frac{-28}{13}\Rightarrow \mathrm{b}=\frac{28}{13}+4=\frac{80}{13}\\ \frac{\mathrm{c}-7}{4}=\frac{-28}{13}\Rightarrow \mathrm{c}=\frac{-28\times 4}{13}+7=-\frac{21}{13}\end{array}$
the  image of point (2,4,7) in given plane  3x – y + 4z = 2 is $\left(-\frac{58}{13},\frac{80}{13},-\frac{21}{13}\right)$
Hence the value of (2a + b + 2c) = $\frac{-116+80-42}{13}=-\frac{78}{13}=-6$