Question

At what point on the curve x = t^3, y = 3t, z = t^4 is the normal plane parallel to the plane 6x+6y-8z=1?

Answer 1

The point on the curve is (x=-1, y=-3, z=1).

Answer 2

I know that but how?

Answer 3

can u plz explain me visually

Answer 4

1)find expression for the tangent vector to the curve
2) find vector normal to the plane (that will be easy)
3)determine when that tangent vector is parallel to that normal vector

v'(t) = 3 t^2 i + 3 j + 4t^3 k (i, j, k are unit vectors)
n-> = 6i + 6k - 8j
m v'(t) = n
solve for t and m. All three components must be equal.
3 t^2 m = 6
3 m = 6
4 t^3 m = - 8
The equation for the 2nd component tells you m=2
The first eqn. tells you t^2 = 1
The third eqn. tells you t^3 = -1
Therefore you know t = -1 is the solution

Answer 5

yahoo

Answer 6

@AccessDenied can u help me to understand

Answer 7

i need visual explanation

Answer 8

lol copying from yahoo isn't the thing http://answers.yahoo.com/question/index?qid=20080624115322AAZyd3F

Answer 9

I don't believe I can do any illustration here justice in the regular 2D plane, let alone 3D. You might be able to view the graph using Wolfram and look at it that way! :P

It may also work to scale down the problem to 2D and remove a z component entirely. I think the principle ends up the same for the most part... but that's a bit of speculating since I don't have as much experience with this particular subject.

Answer 10

Just exactly do you mean by normal plane. x = t^3, y = 3t, z = t^4 is curve in space.

Answer 11

are you ask when the curve normal to the plane or parallel to the plane?

Answer 12

they said to find "1)find expression for the tangent vector to the curve
2) find vector normal to the plane (that will be easy)
3)determine when that tangent vector is parallel to that normal vector "
in this i dont know why we need to find tangent and normal vector to determine the parallel vector

Answer 13

1) did you have your tangent vector?

Answer 14

3 t^2 i + 3 j + 4t^3

Answer 15

\[<3t^2,3,4t^3>\]

Answer 16

r(t) = <3t^2, 3t, 4t^2> is the curve itself

1) r'(t) = <6t, 3, 8t> did have this?

Answer 17

lol ya took the drivative