00:07
Okay, so we're asked to find a tangent vector and normal vector.
00:11
Put a plane curve r of t, or r of t is equal to t to the power of three, one is 4t, comma 5 t squared, minus 2.
00:22
Well, our tangent vector, t of t, is equal to r prime of t divided by a magnitude of r prime of t.
00:35
So let's find r r prime of c first.
00:38
So that's just equal to 3t squared minus 4 comma 10 t.
00:47
Okay, now find a magnitude of our prime of t.
00:51
That's equal to square root of 3t squared minus 4 to the power of 2 plus 10 t squared.
00:59
That gives me 9t4 plus 76t squared plus 16...