Mathematics

The key is recognizing that perpendiculars from $P$ to coordinate planes land at specific points: dropping a perpendicular to the $yz$-plane gives $A(0,b,c)$, and to the $zx$-plane gives $B(a,0,c)$. Now you have three points—the origin $O(0,0,0)$ and two feet of perpendiculars—that determine a unique plane. Use the standard method of finding a plane through three points to get the equation.

The key is recognizing that perpendiculars from $P$ to coordinate planes land at specific points: dropping a perpendicular to the $yz$-plane gives $A(0,b,c)$, and to the $zx$-plane gives $B(a,0,c)$. Now you have three points—the origin $O(0,0,0)$ and two feet of perpendiculars—that determine a unique plane. Use the standard method of finding a plane through three points to get the equation.