Show that any straight line has curvature zero. Conversely, if a smooth curve has curvature zero, then it must be a straight line. Hint: For the first part, recall that any straight line has a position vector F(t) = (a + bt)i + (d + ct)j + (h + kt)k. For the converse, if κ = 0, then T′(t) = 0.
Show that any straight line has curvature zero. Conversely, if a smooth curve has curvature zero, then it must be a straight line. Hint: For the first part, recall that any straight line has a position vector F(t) = (a + bt)i + (d + ct)j + (h + kt)k. For the converse, if κ = 0, then T′(t) = 0.
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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Show that any straight line has curvature zero. Conversely, if a smooth curve has curvature zero, then it must be a straight line. Hint: For the first part, recall that any straight line has a position vector F(t) = (a + bt)i + (d + ct)j + (h + kt)k. For the converse, if κ = 0, then T′(t) = 0.
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