Vector equations ares used to represent the equation of a line or a plane with the help of the variables x, y, z. The vector equation defines the placement of the line or a plane in the three-dimensional framew
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 ...
If we let X = [x y z], we can rewrite the vector X − P in terms of its components, yielding X − P = [ x − Px y − Py z − Pz ] If we let n→=[abc], then we can rewrite the normal-point form of the plane equation as...
结果一 题目 【题目】State the normal vector to the plane with equa (1)2x+3y-z=8(2)3x-y=11(3)z=2(4)x=0 答案 【解析】(1)213(2)10(3)(4)相关推荐 1【题目】State the normal vector to the plane with equa (1)2x+3y-z=8(2)3x-y=11(3)z=2(4)x=0 ...
Step 2: Identify the Normal VectorThe coefficients of x, y, and z in the plane equation represent the components of the normal vector to the plane. Thus, the normal vector n is:n=2i−j+2k Step 3: Write the Position VectorLet r be the position vector of any point (x,y,z) in ...
-9*x + 6*y + 3*z - 12 范例2: # import sympy, Point3D and PlanefromsympyimportPoint3D, 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...
The vector equation of a plane is given by, (r-a).n=0, where a is the position vector of a point on plane and n is the normal vector.Hence, the vector equation is (r- i- j ).(-6 i+6 j+6 k)=0 or r.(-6 i+6 j+6 k)=0 or r.(- i+ j+ k)=0.We have to ...
Newell's method for computing the plane equation of a polygon; 1992. p. 231-2.Tampieri,Filippo. Newell's method for computing the plane equation of a polygon:Graphics Gems, 1994 C . San Diego: Academic Press, 231-232.Filippo Tampieri. 1992. Newell's method for computing the plane ...
To find the vector equation of the plane and its Cartesian form, we can follow these steps:Step 1: Identify the normal vector and distance from the origin The normal vector \( \mathbf{n} \) is given as \( 2 \hat{i} - 3 \hat{j}