The plane $x-y-z=2$is rotated through an angle$90°$ about its line of intersection with the plane$x+2y+z=2$. Then equation of this plane in new position is 

equation of plane is $(x-y-z-2)+\lambda (x+2y+z-2)=0$

$(\lambda +1)x+(2\lambda -1)y+(\lambda -1)z-2\lambda -2=0$

$a_1{a}_2+b_1{b}_2+c_1{c}_2=0\Rightarrow ( \lambda +1)1+(2\lambda -1)(-1)+(\lambda -1)(-1)=0$

$\Rightarrow$equation of plane is $5x+4y+z-10=0$