上图中,矢量n为平面的normal vector(法线的矢量),a为平面上已知点的position vector,r为平面上任意一点的position vector(可理解为整个平面)。从几何学我们知道,法线垂直于平面上任意一条直线,所以法线和平面上任意一条直线的点乘为0(点乘dot product,dot product也可以叫做scalar product)。我们用两个position vector...
(1)with normal vector (bmatrix)2 -1 3(bmatrix) and through (-1,2,4) (2)perpendicular to the line through (2, 3, 1) and (5, 7, 2) and through (3)perpendicular to the line connecting (1,4, 2) and (4, 1, -4) and containing such that (AP):(PB)=1:2 ...
Normal Form: Equation of a plane at a perpendicular distance d from the origin and having a unit normal vector ^nn^ is →r.^nr→.n^ = d. Perpendicular to a given Line and through a Point: The equation of a plane perpendicular to a given vector →NN→, and passing through a point...
To find the equation of a plane that is a distance of 2 units from the origin and has direction ratios of the normal vector as 2,−1,2, we can follow these steps: Step 1: Identify the normal vectorThe direction ratios of the normal vector to the plane are given as 2,−1,2. ...
解析 x+y=2. The direction vectors of the lines are (1,-1,2) and (-1,1,0), so a normal vector for the plane is(-1,1,0)* (1,-1,2)=(2,2,0) and it contains the point (2,0,2). Then an equation of the plane is 2(x-2)+2(y-0)+0(z-2)=0⇔ x+y=2....
# import sympy, Point3D and Plane from sympy import Point3D, Plane # using Plane() p3 = Plane(Point3D(1, 2, 3), normal_vector =(2, 2, 2)) p4 = p3.equation() print(p4) 输出:2*x + 2*y + 2*z - 12 版权属于:月萌API www.moonapi.com,转载请注明出处 本文链接:https://...
Equation of a Plane Point and a Normal Main Concept A plane can be defined by five different methods: A line and a point not on the line Three non-collinear points (three points not on a line) A point and a normal vector Two intersecting lines Two paral
Equation of a Plane: In order to express the equation of a plane, just one point in the plane and one vector that is orthogonal to the plane are enough. The plane equation is derived from the scalar product of the normal vector by whichever vector ...
The scalar equation of a plane is typically written as: {eq}ax + by + cz = d {/eq} Answer and Explanation: To find the scalar equation of the plane, we need to determine the normal vector of the plane. The normal vector is perpendicular to the plane and can......
Plane.equation()方法可以接受以下参数: normal_vector:指定是否返回点法向式方程,默认为False。如果设置为True,则返回点法向式方程;如果设置为False,则返回一般方程。 intercept:指定是否返回截距式方程,默认为False。如果设置为True,则返回截距式方程。 返回的方程对象可以使用str()方法将其转换成字符串形式。