00:01
So they give us this curve and this paraboloid over here, and they want us to figure out where these two will intersect each other.
00:12
So what we can do is the following.
00:17
I'm first going to rewrite our curve in the bracket notation.
00:20
So remember, the i component is going to be x.
00:23
We have no j component, so that's zero.
00:26
And then the k component is going to be 2t minus t squared, or the...
00:31
Z component of it.
00:34
So now what we're going to do is the following.
00:39
I'm going to erase this or erase this z on this side and then put it over here.
00:44
So if these two curves are going to intersect each other, then that means, so remember this is really our x, y, and our z.
00:55
So i'm going to plug in t is equal to x, y is equal to zero, and z is equal to 2 t minus t squared.
01:03
And so i'm going to plug in t is doing that i will get the following equation so t squared plus zero squared is equal to 2t minus t squared now we can solve for what values of t make this true so i'll just rewrite this as t squared is equal to 2t minus t squared and then i'm going to center this a little bit because i don't know something about that is putting me off so we'll have this now now let's move everything over to the left side i'll move it over to the...
01:33
Yeah, move it to the left.
01:34
So it would be 2t squared minus 2t is equal to 0...