Let the image of the point P(1, 2, 3) in the plane 2x – y + z = 9 be Q. if the coordinates of the point R are (6, 10, 7), then the square of the area of the triangle PQR is _______

$\frac{\mathrm{a}-1}{2}=\frac{\mathrm{b}-2}{-1}=\frac{\mathrm{c}-3}{1}=\frac{-2\left[\right(2\left(1\right)-2+3)-9]}{2^2+(-1{)}^2+1^2}$

$\frac{\mathrm{a}-1}{2}=\frac{\mathrm{b}-2}{-1}=\frac{\mathrm{c}-3}{1}=\frac{12}{6}=2 \mathrm{a}=5;\mathrm{b}=0;\mathrm{c}=5$

Q (5, 0, 5)
P (1, 2, 3) 
R(6, 10, 7)

Area $=\frac{1}{2}\left[\right[\overline{\mathrm{PQ}}\times \overline{\mathrm{PR}}]$|              
  $\overline{\mathrm{PQ}}=(4,-2,2), \overline{\mathrm{PR}}=(5,8,4)$

$=\frac{1}{2}\left[\left[\right(4\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}})\times (5\hat{\mathrm{i}}+8\hat{\mathrm{j}}+4\hat{\mathrm{k}}\left)\right]\mid =\frac{1}{2}\left[1188\right]=594\right.$