# Vector parameterization of intersection of 2 surfaces

1. Sep 15, 2010

### musicmar

1. The problem statement, all variables and given/known data
Find a vector parameterization of the intersection of the surfaces x2+y4+2z3=6 and x=y2 in R3.

3. The attempt at a solution

I let x=t.
Then y3=t

I solved the first equation for z in terms of x
z = cube root ((t2+(t(cube rt(t)) - 6)/-2)

I know this is wrong because I checked the back of the book, but I'm not sure how to do it correctly.
Thank you!

2. Sep 15, 2010

### gabbagabbahey

Is your 2nd surface $x=y^2$ or $x=y^3$?

In either case, to avoid taking sqare roots and cube roots of stuff, try letting $y=t$ instead and solving for x.

3. Sep 15, 2010

### musicmar

x=y3, sorry.

So, when y=t, x=t3
and z= cube rt ((-1/2)(t6+t4-6))

This is still wrong. The answer is <t2,t,cube rt(3-t4)>
It doesn't help that I know the answer unless I know how to do it, though.

4. Sep 15, 2010

### gabbagabbahey

Judging from the answer, it looks as though the 2nd surface is supposed to be $x=y^2$, so I'd double check the question if I were you.

5. Sep 15, 2010

### musicmar

thank you. you were right, it was x=y^2.