c) The displacement of a particle in space is given by the vector 7(t) = sint cost i+sin²t j+cost k. Find the tangent, the normal and binormal, and the curvature and torsion of the curve at the points (i) t= 0 and (ii) t = "/2. %3D
c) The displacement of a particle in space is given by the vector 7(t) = sint cost i+sin²t j+cost k. Find the tangent, the normal and binormal, and the curvature and torsion of the curve at the points (i) t= 0 and (ii) t = "/2. %3D
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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Please answer sub c only
![a) Let the 3-D vector a make angles a, ß and y with the coordinate axes. Show that
â = cos ai + cos Bj + cos yk is a unit vector in the direction of the vector a. Show also
that cos²a + cos?B + cos²y = 1.
b) The path of a particle is given by the position vector 7(t) = a sin ti + a cos tj + b tk, where a
and b are real constants.
i) Sketch the graph of the curve traced by the particle as t varies.
ii) Find the length of the curve between the points correspondong to t = 0 and t = 27.
c) The displacement of a particle in space is given by the vector r'(t) = sint cost i+sin²t }+cost k.
Find the tangent, the normal and binormal, and the curvature and torsion of the curve at
the points (i) t= 0 and (ii) t = "/2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95ae200a-d89c-4ac7-875f-557991089bc2%2F553511e2-3b42-46b7-8589-a809bb01698d%2Fmt8dy9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Let the 3-D vector a make angles a, ß and y with the coordinate axes. Show that
â = cos ai + cos Bj + cos yk is a unit vector in the direction of the vector a. Show also
that cos²a + cos?B + cos²y = 1.
b) The path of a particle is given by the position vector 7(t) = a sin ti + a cos tj + b tk, where a
and b are real constants.
i) Sketch the graph of the curve traced by the particle as t varies.
ii) Find the length of the curve between the points correspondong to t = 0 and t = 27.
c) The displacement of a particle in space is given by the vector r'(t) = sint cost i+sin²t }+cost k.
Find the tangent, the normal and binormal, and the curvature and torsion of the curve at
the points (i) t= 0 and (ii) t = "/2.
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