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Find the unit tangent T, the principal normal and binormal B for the space y =t, z =t+ 3 curve x =t –- 3

Find the unit tangent T, the principal normal and binormal B for the space y =t, z =t+ 3 curve x =t –- 3

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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Find the unit tangent T, the principal normal N and binormal B for the space y =t, z=t+' 3 curve x =t- 3
Transcribed Image Text:Find the unit tangent T, the principal normal N and binormal B for the space y =t, z=t+' 3 curve x =t- 3
Expert Solution
Step 1

The given space curve is x=t-t33,y=t2,z=t+t33

Then the vector function will be r(t)→=xi+yj+jk=(t-t33)i+t2j+(t+t33)k

Then r'(t)→=(1-3t23)i+2tj+(1+3t23)k=(1-t2)i+2tj+(1+t2)k

Then 

 

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