考研数学笔记 – 法线
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切线法线

  • 切线斜率 * 法线斜率 = -1

$$
\begin{cases}
f_{\left( x_0 \right)}^\prime * k = -1 \
\
y - y_0 = k \left( x - x_0 \right)
\end{cases}
$$

曲面法线

  • 曲线方程

$$ z = f_{\left( x, y \right)} = 0 $$

  • 点(x0, y0)处的法线

$$
\dfrac{x - x_0}{\frac{\partial z}{\partial x} \mid_{x = x_0}} = \dfrac{y - y_0}{\frac{\partial z}{\partial y} \mid_{y = y_0}}
$$

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