“parametric equations”的概念、定义、习题解题方法及翻译-数学辞典

单词

parametric equations

释义

parametric equations

(of a line in space) Given a line in 3-dimensional space, let (x1,y1,z1) be coordinates of a point on the line, and l, m, n be direction ratios of a direction along the line. Then the line consists of all points P whose coordinates (x,y,z) are given by

for some value of the parameter t. These are parametric equations for the line. They are most easily established by using the vector equation of the line and taking components. If none of l, m, n is zero, the equations can be written

which can be considered to be another form of the parametric equations, or called the equations of the line in ‘symmetric form'. If, say, n = 0 and l and m are both non-zero, the equations are written

if, say, m = n = 0, they become y = y1, z = z1.

More generally in n-dimensional space, if p and a are in Rn with a ≠ 0, then

is a parameterization of the line passing through p which is parallel to a.

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。