本文应用矩阵的运算，给出求二次曲面的切平面方程的一个筒单方法。
From this paper, the equations of tangent planes of a quadratic surface are obtained by matrix operations.
求切平面方程的一般方法是先求切平面的法向量(借助偏导)，再用点法式写出切平面的方程。
The common method to quadric surface equation is to get the Normal Component first, and then write out the equation through dot method.
事实上，代入这些之后，通常可以得到这种形式的值，有时候是t加上一个常数，因为这是你代入平面方程的。
So, in fact, you know, when you plug in these things, normally you get a quantity that's of a form, something times t plus a constant because that's what you plug into the equation of a plane.
当我们已知平面上的两个向量，我们就可以找到，这个平面的法向量，然后我们就可以用法向量来找到方程。
When we know two vectors in a plane, it let us find the normal vector to the plane, and that is what we need to find the equation.
现在在空间中给我三个点，我要找包含这三个点的平面的方程。
Let's say that I'm given three points in space, and I want to find the equation of the plane that contains them.
我在这里画上x - Y坐标平面，画上所有的点满足第一个方程。
And I'm drawing here the X-Y plane. And I'm gonna put, plot all the points that satisfy that first equation.
三维空间中的这两个方程会得到一条线，两平面相交的这条线。
Just the first 2 equations in three dimensions, those give me a line, the line where those two planes meet.
我们用两个方程来描述一条直线,两个方程告诉我们平面相交于直线。
So, we could describe a line by two equations telling us about the two planes that intersect on the line.
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。
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.
记住，线性方程组问题，可以理解为求三个平面的交，因为每个方程就是一个平面。
So, remember, in the linear system, you can think of a linear system as asking you to find the intersection between three planes because each equation is the equation of a plane.
有两种可能，一是方程组可逆，这就是一般情况了，这时三个平面交于一点。
And then, we have two cases. So, the case where the system is invertible corresponds to the general situation where your three planes somehow all just intersect in one point.
水平面上的方程，都是z等于某个常数的形式，等等。，z，equals，zero，z，equals，one，，z，equals，two，，and，so，on。,函数的图像,在那里就是这样的表现。
So, horizontal planes have equations of a form z equals some constant, z=0 z=1 z=2 So, maybe the graph of my function will be some sort of plot out there.
用边界元方法求解平面拉普拉斯方程时必须计算两个矩阵。
Two matrices have to be calculated when solving plane Laplace equation by the use of BEM.
采用平面四边形为基本封闭形建立位移方程，给出了所有四个基本类型的解。
A planar quadrilateral is adopted as the basic loop in building up the displacement equations, and four basic types of solutions are given.
给出一个适用于平面断裂力学分析的新边界积分方程，在此方程的基础上建立了边界元数值计算方法。
A new boundary integral equation is introduced to analyze plane elastic problems with cracks, and the boundary element numerical method based on this equation is established.
运用复变函数及积分方程方法，求解了半平面域多圆孔多裂纹反平面问题。
By using of complex variable function and integral equation method, the antiplane multiple holes and cracks problem of half plane region is considered in this paper.
提出一种在绝对坐标系中建立小应变有限转动平面梁动力学方程的有效方法。
An effective method is presented to derive the equations of finite-rotation plan beams.
然后根据上述知识，利用点的速度合成定理推导出车削平面传动比的方程。
And then the equation of transmission ratio for machining plane was deduced by using the referred information.
根据各向异性矩形板平面应力问题的基本方程精确地求得了位移函数的一般解。
Based on the fundamental equation of an anisotropic rectangular plate in plane stress problem, an accurate general displacement solution is obtained.
并由刚体平面运动方程，推导出混凝土护坡板的绝对稳定和准稳定条件关系式，以确定护坡板的尺寸。
The formulas are derived for the conditions of concrete blocks absolute-stability and quasi-stability according to the equations of stiff-body motion on plane.
在此基础上利用微分方程相平面理论分析表面油流谱的局部特性和对流谱局部地进行分类。
The local behavior of the surface oil flow patterns is analyzed with phase plane theory of ordinary differential equations. Also the surface oil flow patterns are locally classified.
本文介绍了一种平面流动的快速欧拉方程解法。
A fast Euler Solver for planar flows is developed in this paper.
给出主参数共振系统参数平面的分岔集和幅频响应方程的分岔图。
The bifurcation diagrams of the parameter plane and the response equation are obtained.
文章主要讨论了空间曲线在一般平面上的射影柱面方程的求法。
This paper discusses the solutions of the equations of a class of projective cylinders formed by space curves onto general planes.
采用迭代法求解转向平面运动方程，计算结果与实车实验进行了对比。
The turning plane motion equations are solved by means of iterations, and on-vehicle experiment was carried out in order to compare with theoretical results.
通过分析导弹在导引段的纵向平面运动方程和侧向平面运动方程的特点，设计了实现垂直打击任务的制导逻辑。
On analyzing the longitudinal plane motion equation and lateral plane motion equation in guided phase, the guidance logic for perpendicular impact task was devised.
从由曲线普通方程求平面图形面积的公式出发推出在各种情形下由曲线参数方程求平面图形面积的公式。
From commonly used equation of calculating plane figure quadrature, formulas of calculating plane figure quadrature by applying curve parametric equation can be deduced.
利用流体运动方程和平面强旋转流的流动特性分析了涡流分级机内空气流动特性和气固两相流运动特性。
The characteristics of air flow and the air-solid two phase movement in a turbo classifier are analyzed by the dynamic equation of fluid motion combined with the features of intense circulating flow.
本文应用一般型谐振腔的变分方程，推导了平面型谐振腔谐振频率的特征方程。
The variational equation for general resonant cavities is used to derive the characteristic formula for the resonant frequency of the arbitrarily planar reso aators.
按平面应力问题，直接从压电物理方程出发，导出了压电梁的状态方程。
The state equation of Pieoelectric beam is deduced directly from a piezoelectric physical equation in terms of a plane stress problem.
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