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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
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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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
Transcribed Image Text: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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