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.
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。
Let's say that I'm given three points in space, and I want to find the equation of the plane that contains them.
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。
And I'm drawing here the X-Y plane. And I'm gonna put, plot all the points that satisfy that first equation.
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。
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.
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。
Well, for example,if our surface is a plane, a slanted plane given by some equation, ax by cz = d.
比如说，假如我们的曲面是一个平面，由公式ax+by+cz=d给出的，一个倾斜的平面。
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.
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, let's say that we take still the same line up there, x+2y+4z=7 and let's consider the plane with the equation x+2y+4z = 7.
我们还是看之前的那条直线，同时考虑平面。
Two matrices have to be calculated when solving plane Laplace equation by the use of BEM.
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。
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.
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。
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.
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。
An equation for the calculation of true shear strain was derived from the integration of infinitesimal shear strain in plane shearing process with constant principal shear strain direction.
对切应变主轴不变的平面简单切变过程，通过无穷小应变的积分，导出了真实切应变计算公式。
And then the equation of transmission ratio for machining plane was deduced by using the referred information.
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。
Based on the fundamental equation of an anisotropic rectangular plate in plane stress problem, an accurate general displacement solution is obtained.
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。
The general equation of heat transfer in the stationary state is solved for four special forms of bodies, namely, plane, circular cylinder, sphere, and prolate spheroid.
接着详细研究了在稳定的情形下普遍传热方程在四种特殊形状的物体中的解，这四种特殊形状是，平面、圆柱体、球体、和长椭球。
The symmetry algebras of 1 + 1 dimensional nonlinear evolution equation arising from the motion of plane curve in affine geometry are systematically studied.
系统地研究了来自于射影几何中平面曲线运动的1 + 1维非线性方程的对称代数。
According to the dynamic equation of relative motion between the missile and the target, Lyapunov stability theory is used to design a new yaw plane guidance law for missiles.
根据导弹与目标之间的相对运动方程，应用李雅普·诺夫稳定性理论设计一种新的导弹航向平面导引律。
The analytical method of system of plane intercrossing forces is to calculate unknown forces by use of equilibrium equation of plane system of plane intercrossing forces.
平面汇交力系的解析法是用平面汇交力系的平衡方程计算未知力，其平衡方程最简单，但也最容易出错。
Based on the averaged equation, the transition boundaries are sought to divide the parameter plane into different regions, corresponding to different types of the solutions.
基于平均方程，得到了参数平面上的转迁集，这些转迁集将参数平面划分为不同的区域，在各个不同的区域对应于系统不同的解。
In deriving the integral equation, the convergence of series is modified by application of the plane Gauss Theorem.
在建立积分方程时，运用平面高斯定理改善了级数的收敛性。
According to principle of plane engagement, the paper deduces the equation of conjugate tooth outline in workpiece from given double-arc tooth outline of hob.
根据平面啮合原理，由给定的滚刀双圆弧齿形，推导出与其共轭的工件齿形方程。
The problem of attaining the tangent equation of a certain point on a quadratic curve is basically solved in plane analytical geometry.
平面解析几何对“求过二次曲线外的点所引曲线切线的方程”的问题，未给出一般的方法和公式。
On analyzing the longitudinal plane motion equation and lateral plane motion equation in guided phase, the guidance logic for perpendicular impact task was devised.
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。
From commonly used equation of calculating plane figure quadrature, formulas of calculating plane figure quadrature by applying curve parametric equation can be deduced.
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。
The state equation of Pieoelectric beam is deduced directly from a piezoelectric physical equation in terms of a plane stress problem.
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 moments of momentum of plane motion rigid body in three different situations are analyzed and discussed and general form of equation of moment of momentum is obtained.
对三种情况下平面运动刚体的动量矩进行了分析和讨论，得到一般形式的动量矩方程。
Two-point form of straight-line equation is a mathematical model delineating the straight line joined by any two points in a plane.
两点式直线方程是描述平面上任意两点所连直线的一个数学模型。
A integrated equation set for solving plane parallel motion of rigid body was derived, and the conditions of system of forces simplified on the center of mass plane was discussed.
给出了解决刚体平面平行运动问题的一组完整方程，讨论了力系简化在质心平面内的条件。
Based on the equivalent elasticity method, the plane coupling vibration of a rectangular piezoelectric ceramic plate was studied and the resonant frequency equation was derived out.
利用等效弹性法分析了压电矩形共振器的二维耦合振动，导出了振子共振频率的解析表达式。
Based on plane wave decomposition, We propose a wave-equation depth migration method for pre-stack seismic data.
提出了一套基于平面波分解的波动方程叠前地震数据深度偏移方法。
In this paper, the interaction between a cw plane wave and a plane pulse travelling with sound speed is considered. Both of them satisfy the homogeneous wave equation.
本文讨论一列平面波与一列平面行波脉冲的声相互作用，显然这两个波不仅都满足波动方程，而且可以用来讨论公共区之外的声散射声问题。
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