- #1
EnchantedEggs
- 27
- 0
Hi all,
When you have a surface defined by [itex] F(x, y, z) = 0 [/itex] where [itex]x = f(t)[/itex], [itex]y= g(t)[/itex] and [itex]z= h(t)[/itex] and a point on this surface [itex] P_0 = (x_0, y_0, z_0) [/itex], could someone explain to me why a line through [itex] P_0 [/itex] with direction numbers [itex] [\frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt}] [/itex] is perpendicular to a line through [itex] P_0 [/itex] with direction numbers [itex] [\frac{\partial F}{dx}, \frac{\partial F}{dy}, \frac{\partial F}{dz}] [/itex]?
I'm having real trouble picturing it in my head, which means I'm struggling to understand why it is so.
Thanks!
When you have a surface defined by [itex] F(x, y, z) = 0 [/itex] where [itex]x = f(t)[/itex], [itex]y= g(t)[/itex] and [itex]z= h(t)[/itex] and a point on this surface [itex] P_0 = (x_0, y_0, z_0) [/itex], could someone explain to me why a line through [itex] P_0 [/itex] with direction numbers [itex] [\frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt}] [/itex] is perpendicular to a line through [itex] P_0 [/itex] with direction numbers [itex] [\frac{\partial F}{dx}, \frac{\partial F}{dy}, \frac{\partial F}{dz}] [/itex]?
I'm having real trouble picturing it in my head, which means I'm struggling to understand why it is so.
Thanks!