Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Why are these perpendicular?

**Physics Forums - The Fusion of Science and Community**