- #1
Ian_Brooks
- 129
- 0
Not a homework question
say we have a curve f(x,y,z)
and the tangent plane to the curve at a point (xo,yo,zo) is given by
[tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(x-xo) + [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(y-yo) + [tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(z-zo) = 0
then would the normal plane to the curve be either of the following?
[tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(z-zo) = 0
[tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(z-zo) = 0
[tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(z-zo) = 0
[tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(z-zo) = 0
say we have a curve f(x,y,z)
and the tangent plane to the curve at a point (xo,yo,zo) is given by
[tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(x-xo) + [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(y-yo) + [tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(z-zo) = 0
then would the normal plane to the curve be either of the following?
[tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(z-zo) = 0
[tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(z-zo) = 0
[tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(z-zo) = 0
[tex]\frac{{\partial d}}{{\partial z}}[/tex](xo,yo,zo)(x-xo) - [tex]\frac{{\partial d}}{{\partial y}}[/tex](xo,yo,zo)(y-yo) - [tex]\frac{{\partial d}}{{\partial x}}[/tex](xo,yo,zo)(z-zo) = 0