问题
已知积分区域 $D$ 的面积为 $A$, 则以下选项中,正确的是哪个?选项
[A]. $\iint_{D}$ $1$ $\mathrm{~d} \sigma$ $=$ $-A$[B]. $\iint_{D}$ $1$ $\mathrm{~d} \sigma$ $=$ $A$
[C]. $\iint_{D}$ $1$ $\mathrm{~d} \sigma$ $=$ $A^{2}$
[D]. $\iint_{D}$ $1$ $\mathrm{~d} \sigma$ $=$ $1$
则以下选项中,正确的是哪个?
$\boldsymbol{n}_{1}$ $=$ $\left(F_{x}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), F_{y}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), F_{z}^{\prime}\left(x_{0}, y_{0}, z_{0}\right)\right)$
$\boldsymbol{n}_{1}$ $=$ $\left(G_{x}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), G_{y}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), G_{z}^{\prime}\left(x_{0}, y_{0}, z_{0}\right)\right)$
该点处的切向量为:
$\boldsymbol{\tau}$ $=$ $\boldsymbol{n}_{1} \times \boldsymbol{n}_{2}$
若记切向量 $\boldsymbol{\tau}$ $=$ $(A, B, C)$,
则曲线 $\Gamma$ 在点 $(x_{0}, y_{0}, z_{0})$ 处的法平面方程是多少?
$\boldsymbol{n}_{1}$ $=$ $\left(F_{x}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), F_{y}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), F_{z}^{\prime}\left(x_{0}, y_{0}, z_{0}\right)\right)$
$\boldsymbol{n}_{1}$ $=$ $\left(G_{x}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), G_{y}^{\prime}\left(x_{0}, y_{0}, z_{0} \right), G_{z}^{\prime}\left(x_{0}, y_{0}, z_{0}\right)\right)$
该点处的切向量为:
$\boldsymbol{\tau}$ $=$ $\boldsymbol{n}_{1} \times \boldsymbol{n}_{2}$
若记切向量 $\boldsymbol{\tau}$ $=$ $(A, B, C)$,
则曲线 $\Gamma$ 在点 $(x_{0}, y_{0}, z_{0})$ 处的切线方程是多少?