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(Solved): Class Participation 2 Pret:1* July_2025 on CAMYAS Example: 2 Consider f(x,y)=\sqrt(x^(2) y^(2)) (a ...



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!



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