在某个问题中，法线n被指定为2i+j-k，平面上已知点a的坐标为-3i+2j+5k。代入公式得到r·（2i+j-k）=-9，进而得到平面r的表达式为2x+y-z=-9，这种形式表示一个平面，即cartesian form。考虑另一个问题，其中平面的法线（a，b，c）为（2 ，-4，-1），且平面上有经过点（1,-2,5）。
Maths---vector of plane 平面的矢量表达式 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...
Derive a Vector Form for Snell's LawThe equation I've given here shows the unit vector in the direction of the refracted ray as the vector addition of a component along the surface in the plane of incidence and a component along the surface normal. I prefer to work with all of these ...
(2)ⅱ -5x+3y+12z=12 (3)ⅱ -y+z=3 {many vector forms exist} 反馈 收藏
independent的vector做basis， 比如(2,3,4) - (-2,1,5) = (4, 2, -1), (-1, 1, 1).再随便找个起点，比如(-2, 1, 5)所以该平面就是(-2 +4a -b, 1 + 2a + b, 5 -a +b)另外，vector只有方向，没有起点，不存在神马vector of line共起点这一说 ...
vectorplanenormalembed向量alpha 平面的法向量(Thenormalvectoroftheplane) Normalvectorofplane WushanthirdWangJianhua Inrecentyears,inthereformofnewtextbooks,spacevectors areintroducedintosolidgeometry,whichmakescoordinate, regular,symbolicandquantitativeofgeometricproblems,and transformscomplexreasoningintoalgebraicoperation...
R.I. Bogdanov, Reduction to orbital normal form of a vector field on the plane, Funct. Anal. Appl. 10 (1976) 61–62.R.I. Bogdanov, Reduction to orbital normal form of a vector field on the plane, Funct. Anal. Appl. 10 (1976) 61-62....
In this explainer, we will learn how to convert between rectangular and polar forms of a vector. When we think about vectors in the plane, we usually think of Cartesian coordinates as this is the most prevalent coordinate system, which leads to the rectangular form of a vector. In ...
Symmetry degree is utilized to characterize the asymmetry of a physical system with respect to a symmetry group. The scalar form of symmetry degree (SSD) based on Frobenius-norm has been introduced recently to present a quantitative description of symmetry. Here we present the vector form of the...
That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicity, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding (n-1)-form. ...