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!
