单词

line

释义

line

(in three dimensions) As in two dimensions there are a number of standard formats which can be used.

Two‐point form.

The condition that the general point P(x,y,z) lies on the line through A(x1,y1,z1) and B(x2,y2,z2) is equivalent to requiring the direction ratios of AP and AB being equal. That is:

Parametric vector form.

If the vector (l,m,n) is parallel to the line and the point A(x1,y1,z1) lies on it, the position vector of a general point P on the line has the form

If a and b are the position vectors of points A and B on the line, the position vector of a general point is

Vector form.

The equation r = a + λ(b−a) can be rewritten as (r−a)×(b−a) = 0, where × denotes the vector product. More generally the equation

defines a line when a ≠ 0 and a⋅b = 0. This line is parallel to a and passes through the point (a × b)/|a|2.

随便看

数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。