Suppose you have a line with corresponding equation ax +by+c= 0; also suppose you have points (s, t) and (u, v) not on l. Write the parameterization of the line m passing through (s, t) and (u, v) and use it to show that (s, t) and (u, v) are on opposite sides of & if and only if there is a rational A between 0 and 1 so that the parameterization of m at A is on the line l.
Suppose you have a line with corresponding equation ax +by+c= 0; also suppose you have points (s, t) and (u, v) not on l. Write the parameterization of the line m passing through (s, t) and (u, v) and use it to show that (s, t) and (u, v) are on opposite sides of & if and only if there is a rational A between 0 and 1 so that the parameterization of m at A is on the line l.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose you have a line ` with corresponding equation ax + by + c = 0; also suppose you have points
(s, t) and (u, v) not on `. Write the parameterization of the line m passing through (s, t) and (u, v)
and use it to show that (s, t) and (u, v) are on opposite sides of ` if and only if there is a rational λ
between 0 and 1 so that the parameterization of m at λ is on the line `
Transcribed Image Text:Suppose you have a line with corresponding equation ax +by+c= 0; also suppose you have points
(s, t) and (u, v) not on l. Write the parameterization of the line m passing through (s, t) and (u, v)
and use it to show that (s, t) and (u, v) are on opposite sides of & if and only if there is a rational A
between 0 and 1 so that the parameterization of m at A is on the line l.
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