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Consider the curve C with parametrisation where t E R. r(t) = cos(5t) cosh(t) -i+ sin(5t) cosh(t) -j+tanh(t)k, (a) Show that C lies on the surface of the sphere described by the equation x² + y² + z² = 1. (b) Find the vector equation of the line L that is tangent to C at the point r(0).

Consider the curve C with parametrisation where t E R. r(t) = cos(5t) cosh(t) -i+ sin(5t) cosh(t) -j+tanh(t)k, (a) Show that C lies on the surface of the sphere described by the equation x² + y² + z² = 1. (b) Find the vector equation of the line L that is tangent to C at the point r(0).

Advanced Engineering Mathematics
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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Consider the curve C with parametrisation where t E R. r(t) = = cos(5t) cosh(t) i+ sin(5t) cosh(t) -j+tanh(t)k, (a) Show that C lies on the surface of the sphere described by the equation x² + y² + z² = 1. (b) Find the vector equation of the line L that is tangent to C at the point r(0).
Transcribed Image Text:Consider the curve C with parametrisation where t E R. r(t) = = cos(5t) cosh(t) i+ sin(5t) cosh(t) -j+tanh(t)k, (a) Show that C lies on the surface of the sphere described by the equation x² + y² + z² = 1. (b) Find the vector equation of the line L that is tangent to C at the point r(0).
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