) If the gradient of ff is ∇f=xi⃗ +yj⃗ +3zyk⃗ ∇f=xi→+yj→+3zyk→ and the point P=(−6,−6,−2)P=(−6,−6,−2) lies on the level surface f(x, y,z)=0f(x, y,z)=0, find an equation for the tangent plane to the surface at the point PP.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.