1. Consider the position vector r = xi+yj+zk of a particle moving in some space curve defined by the following parametric equations: 2²₁₁z=t+2. 2t+1 +y=1 x = i,j,k are the standard unit vectors in rectangular coordinates, x,y, and z are the rectangular position coordinates, and t is the time parameter. Determine: (a) the velocity vector v, (b) the acceleration vector a, (c) the unit tangent vector T for the space curve, (d) the unit normal N for the space curve, (e) the unit bi- normal vector B (=TXN) for the space curve, (f) evaluate T,N, and B at t = 2. ANSWER ONLY A B C

1. Consider the position vector r = xi+yj+zk of a particle moving in some space curve defined by the following parametric equations: 2²₁₁z=t+2. 2t+1 +y=1 x = i,j,k are the standard unit vectors in rectangular coordinates, x,y, and z are the rectangular position coordinates, and t is the time parameter. Determine: (a) the velocity vector v, (b) the acceleration vector a, (c) the unit tangent vector T for the space curve, (d) the unit normal N for the space curve, (e) the unit bi- normal vector B (=TXN) for the space curve, (f) evaluate T,N, and B at t = 2. ANSWER ONLY A B C

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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Additional question:

Where does the space curve lies, e.g. does the particle motion lie in a plane? If so, what does that imply about T, N, and B?

1.
Consider the position vector r = xi+yj+zk of a particle moving in some
space curve defined by the following parametric equations:
x = 2+1, y = ₁₁2=t+ 2.
t-1
i,j,k are the standard unit vectors in rectangular coordinates, x,y, and z are the
rectangular position coordinates, and t is the time parameter.
Determine: (a) the velocity vector v, (b) the acceleration vector a, (c) the unit tangent
vector T for the space curve, (d) the unit normal N for the space curve, (e) the unit bi-
normal vector B (=TXN) for the space curve, (f) evaluate T,N, and B at t = 2.
ANSWER ONLY A B C

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