密切平面

${\displaystyle (R-r(t_{0}),r'(t_{0}),r''(t_{0}))=0}$

其中 R ＝ {X,Y,Z}表示P点的密切平面上任意一点的向径。

上式也可用行列式表示为 ${\displaystyle {\begin{vmatrix}X-x(t_{0})&Y-y(t_{0})&Z-z(t_{0})\\x'(t_{0})&y'(t_{0})&z'(t_{0})\\x''(t_{0})&y''(t_{0})&z''(t_{0})\end{vmatrix}}=0}$

${\displaystyle (R-r(s_{0}),{\dot {r}}(s_{0}),{\ddot {r}}(s_{0}))=0}$ 其中${\displaystyle r=r(s)}$.

上式也可用行列式表示为 ${\displaystyle {\begin{vmatrix}X-x(s_{0})&Y-y(s_{0})&Z-z(s_{0})\\{\dot {x}}(s_{0})&{\dot {y}}(s_{0})&{\dot {z}}(s_{0})\\{\ddot {x}}(s_{0})&{\ddot {y}}(s_{0})&{\ddot {z}}(s_{0})\end{vmatrix}}=0}$