$\text{ The plane }2x+y+2z=9\text{ intersects the coordinate axes }$$\text{ at }A,B,C.\text{ The orthocentre of the triangle }ABC\text{ is }$

$A=\left(\frac{9}{2},0,0\right),B=(0,9,0),C=\left(0,0,\frac{9}{2}\right)$

$\text{ If }O(\alpha ,\beta ,\gamma )\text{ is the orthocentre, }AO\perp BC\text{, }$

$BO\perp CA,CO\perp AB,\Rightarrow \alpha =\gamma =2\beta .(\alpha ,\beta ,\gamma )\text{ is a point on the }$

$\text{ given plane }\Rightarrow \alpha =\gamma =2,\beta =1$

$\therefore O\equiv (2,1,2)$