Using appropriately labelled diagrams to support your answer, explain in detail how the position vector r(t) of a point P(x, y, z) in R³, on a space curve C, yields the following important results, r' (t) Ir' (t) and explain in your own words how the notion of the derivative is involved, i.e, r(t+h) - r(t) (a) The unit tangent vector T(t) = r' (t)= lim h-0 (b) Using a clear diagram explain how we use the unit tangent vector T(t) to find the normal and binormal vectors, N(t) and B(t), respectively. (c) If r(t)= c, a constant, prove that r' (t) is orthogonal to r(t), and also that, r' (t) x r(t) = 0.
Using appropriately labelled diagrams to support your answer, explain in detail how the position vector r(t) of a point P(x, y, z) in R³, on a space curve C, yields the following important results, r' (t) Ir' (t) and explain in your own words how the notion of the derivative is involved, i.e, r(t+h) - r(t) (a) The unit tangent vector T(t) = r' (t)= lim h-0 (b) Using a clear diagram explain how we use the unit tangent vector T(t) to find the normal and binormal vectors, N(t) and B(t), respectively. (c) If r(t)= c, a constant, prove that r' (t) is orthogonal to r(t), and also that, r' (t) x r(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
Related questions
Question
Asap
Transcribed Image Text:Q.2
Using appropriately labelled diagrams to support your answer, explain in detail how the
position vector r(t) of a point P(x, y, z) in R³, on a space curve C, yields the following
important results,
T' (t)
Ir' (t)|
how the notion of the derivative is involved, i.e,
r(t+h)- r(t)
r' (t) = lim
(a) The unit tangent vector T(t) =
and explain in your own words
(b) Using a clear diagram explain how we use the unit tangent vector T(t) to find the
normal and binormal vectors, N(t) and B(t), respectively.
(c) If r(t) = c, a constant, prove that r' (t) is orthogonal to r(t), and also that,
r"(t) x r(t) = 0.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
