I am asked to parametrize the following;
Plane above the square
The portion of the plane \(\displaystyle 4x + 2y + 4z = 12\) that lies above the square; \(\displaystyle 0 \le x \le 2\;and\;0 \le y \le 2\) in the first quadrant.
Here is what I came up with.
\(\displaystyle \[Let\;u = x\;and\;y = v\;then,\;\quad r(u,v) = ui\limits^ \wedge + vj\limits^ \wedge + (3 - u - \frac{v}
{2})k\limits^ \wedge
\]\)
But I have no clue how to come up with the limits of u and v. The word "portion" kind of make me think there is an outer limit. But then again I know that a plane goes to infinity without outer limits.
At the same time though, I was thinking that it wants only the "PORTION" in the first quadrant.
Any help would be appreciated.
Plane above the square
The portion of the plane \(\displaystyle 4x + 2y + 4z = 12\) that lies above the square; \(\displaystyle 0 \le x \le 2\;and\;0 \le y \le 2\) in the first quadrant.
Here is what I came up with.
\(\displaystyle \[Let\;u = x\;and\;y = v\;then,\;\quad r(u,v) = ui\limits^ \wedge + vj\limits^ \wedge + (3 - u - \frac{v}
{2})k\limits^ \wedge
\]\)
But I have no clue how to come up with the limits of u and v. The word "portion" kind of make me think there is an outer limit. But then again I know that a plane goes to infinity without outer limits.
At the same time though, I was thinking that it wants only the "PORTION" in the first quadrant.
Any help would be appreciated.