After the formula of documents are used to rewrite elements of Jacobian matrix, the vector cross product is changed into the vector dot product in Jacobian matrix.

利用现有的公式对雅可比矩阵中的元素进行改写，将矢量叉乘变为矢量点乘。

youdao

OK, now, so there's an interesting thing to note, which is that we can use the usual product rule for derivatives with vector expressions, with dot products or cross products.

还有个很有趣的现象要注意一下，就是我们可以用乘积法则,对向量表达式求导，无论是点乘或叉乘。

youdao

Another way to do it, of course, would provide actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane.

当然也有另一种方法，就是用参数方程表示这两条直线，用两条直线的方向向量作外积，从而得到切平面的法向量。

youdao