`(S): (x-3)^2+y^2+(z-2)^2=25`

`=>` `{("Tâm"\ I(3;0;2)),("Bán kính"\ R=sqrt(25)=5=IA=IB):}`

Ta có: `{(vec(u_(Delta))=(1;2;2)),(M(-1;-2;-3) in Delta=> vec(IM)=(-4;-2;-5)):}`

`=>` `[vec(u_(Delta)), vec(IM)]=(-6; -3; 6)`

`S_(triangle IAB)=1/2*IH*AB`

Mà `IH=d(I,Delta)=(|[vec(u_(Delta))","\ vec(IM)]|)/(|vec(u_(Delta))|)=(sqrt(6^2+3^2+6^2))/(sqrt(1^2+2^2+2^2))=3`

`=>` `S_(triangle IAB)=1/2*IH*AB=1/2*3*2AH=3*sqrt(IA^2-IH^2)=3sqrt(5^2-3^2)=12 (đvdt)`

`=>` $\fbox{Đúng}$