the line through the points p and q is formed with "p + λ(q − p)." Why is the direction given by q-p and not q+p or something else
the line through the points p and q is formed with "p + λ(q − p)." Why is the direction given by q-p and not q+p or something else
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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the line through the points p and q is formed with "p + λ(q − p)." Why is the direction given by q-p and not q+p or something else
Expert Solution
Step 1: Step 1.
The expression "p + λ(q - p)" represents a parametric equation for a line passing through points P and Q, where p and q are positive vectors of P and Q and λ is a parameter that varies to trace points along the line.
The direction vector q - p is used because it describes the direction from point P to point Q. By substrating P from Q, you get a vector pointing from P to Q. By multiplying this direction vector by λ and adding it to point P, you can traverse the line in the direction from P to Q.
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