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s3a
 4 years ago
(a) What is the equation of the tangent plane to the surface
z = 2xy + 3y^2 + 2x + y + 4
at the point P(4,3,60)?
(b) What are the parametric equations of the normal line at this point?
s3a
 4 years ago
(a) What is the equation of the tangent plane to the surface z = 2xy + 3y^2 + 2x + y + 4 at the point P(4,3,60)? (b) What are the parametric equations of the normal line at this point?

This Question is Closed

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0For (a), I get z = 12x 25y  63 For (b), I get that the constant are 4, 3, and 60 for x, y, and z respectively but, I don't know how to find the coefficients of t for x, y, and z and would appreciate it if someone could help me figure this out.

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0Basically, I get it all except the coefficients of t for part (b).

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0you might want to try part (a) again

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0My answer is correct. I checked.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0did you type the question correctly....(4,3,60) is not a solution to the equation you gave above

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0Sorry, z != 2xy + 3y^2 + 2x + y + 4 z = x^2 + 2xy + 3y^2 + 2x + y + 4

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0do you know how to find the normal vector to the plane?

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0and do you mean *a* normal vector?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0no that is not a normal vector to the surface

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0\[a(xx_0)+b(yy_0)+c(zz_0)=0\] is a plane with normal vector \(\vec{n}=<a,b,c>\)

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0find the coefficients infront of the x,y,z variables

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0Oh wait! Is the normal vector: 12 i + 25 j + k ?

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0(I did that based on what you just said.)

s3a
 4 years ago
Best ResponseYou've already chosen the best response.0Oh so the coefficients of t are the coefficients of i, j, k.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.0don't forget to include your original point (4,3,60)
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