Riemann surface
matlab

Problem 1.4
The cross-product of any two vectors in the plane will give a vector perpendicular to the plane. For example, we might pick the base $(\mathbf{A})$ and the left side $(\mathbf{B})$ :
$$\mathbf{A}=-1 \hat{\mathbf{x}}+2 \hat{\mathbf{y}}+0 \hat{\mathbf{z}} ; \mathbf{B}=-1 \hat{\mathbf{x}}+0 \hat{\mathbf{y}}+3 \hat{\mathbf{z}}$$

$$\mathbf{A} \times \mathbf{B}=\left|\begin{array}{ccc} \hat{\mathbf{x}} & \hat{\mathbf{y}} & \hat{\mathbf{z}} \ -1 & 2 & 0 \ -1 & 0 & 3 \end{array}\right|=6 \hat{\mathbf{x}}+3 \hat{\mathbf{y}}+2 \hat{\mathbf{z}}$$
This has the right direction, but the wrong magnitude. To make a unit vector out of it, simply divide by its length:
$|\mathbf{A} \times \mathbf{B}|=\sqrt{36+9+4}=7$.
$$\hat{\mathbf{n}}=\frac{\mathbf{A} \times \mathbf{B}}{|\mathbf{A} \times \mathbf{B}|}=\frac{6}{7} \hat{\mathbf{x}}+\frac{3}{7} \hat{\mathbf{y}}+\frac{2}{7} \hat{\mathbf{z}}$$

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