Class Participation 2 Pret:1* July_2025 on CAMYAS Example: 2 Consider
f(x,y)=\sqrt(x^(2) y^(2))
(a) Find the equation of a tangent plane at point (
3,4,5
). (b) Find the normal vector at (3, 4, 5). (c) Find the parametric equations of normal lines at (
3,4,5
). (d) (i) Find the angle between the tangent plane at (
3,4,5
) and the
xy
-plane. (ii) Find the angle between the tangent plane at
(3,4,5)
and the plane
z=-x 2y
. Solution: Given
f(x,y)=\sqrt(x^(2) y^(2))
. Set
z=f(x,y)
. Then
z=\sqrt(x^(2) y^(2))
, i.e.,
z-\sqrt(x^(2) y^(2))=0
Then
z-f(x,y)=0=>z-\sqrt(x^(2) y^(2))=0
. Set
F(x,y,z)=z-\sqrt(x^(2) y^(2))
. The level surface is
S:F(x,y,z)=0
. Now,
F(x,y,z)=z-\sqrt(x^(2) y^(2))
. Please complete!