Parametric Surfaces Homework Help

[goonking]

Homework Statement

Homework Equations

The Attempt at a Solution

so to start this off, I choose a random point, by setting u and v = 0

giving me the point (0,3,1) but I have no idea how what to do next.

how do I find ua and vb?

 

[tommyxu3]

Thinking directly, ##a## and ##b## must be to vectors lying on the plane. Maybe you can set they start at ##r_0,## that is your ##(0,3,1)## and find any two independent vector to structure the plane.

 

[goonking]

Thinking directly, ##a## and ##b## must be to vectors lying on the plane. Maybe you can set they start at ##r_0,## that is your ##(0,3,1)## and find any two independent vector to structure the plane.

sorry, a bit confused. do I plug in more numbers for v and u?

 

[tommyxu3]

##v## and ##u## then are parameter. Selected ##a## and ##b## will dominate the form of the plane.

 

[Ray Vickson]

Homework Statement

View attachment 89508

Homework Equations

View attachment 89509

The Attempt at a Solution

so to start this off, I choose a random point, by setting u and v = 0

giving me the point (0,3,1) but I have no idea how what to do next.

how do I find ua and vb?

If ##(x,y,z)## are the cartesian coordinates of a point on the surface, how do you express the values of ##x##, ##y## and ##z## in terms of the parameters ##u## and ##v##? Can you use those expressions to re-write the surface in the form ##z = a + b x + cy##?

 

[goonking]

If ##(x,y,z)## are the cartesian coordinates of a point on the surface, how do you express the values of ##x##, ##y## and ##z## in terms of the parameters ##u## and ##v##? Can you use those expressions to re-write the surface in the form ##z = a + b x + cy##?

how did you think of the form ##z = a + b x + cy##? does the surface have to be in that form?

 

[goonking]

how did you think of the form ##z = a + b x + cy##? does the surface have to be in that form?

anyway, the textbook came up with

= <0,3,1> + u<1,0,4> + v<1,-1,5> and I have no idea how they came up with u<1,0,4> and v<1,-1,5>.

how are they coming up with vectors with just a given point?!

 

[Ray Vickson]

anyway, the textbook came up with

= <0,3,1> + u<1,0,4> + v<1,-1,5> and I have no idea how they came up with u<1,0,4> and v<1,-1,5>.

how are they coming up with vectors with just a given point?!

What are ##\bf{i}, \bf{j}## and ##\bf{k}##?

 

[goonking]

What are ##\bf{i}, \bf{j}## and ##\bf{k}##?

i = <0,3,1>
j= u<1,0,4>
k=v<1,-1,5>

 

[tommyxu3]

They are unit vectors on the three dimension instead of what you say. The solution makes it to the form to match the required.