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Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P. 3 3 r(t) = (3 cos t, 3 sin t, 9), PG-

Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P. 3 3 r(t) = (3 cos t, 3 sin t, 9), PG-

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 vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P. 3 r(t) = (3 cos t, 3 sin t, 9), P(G 9) Step 1 The unit tangent vector T(t) att is defined as follows: r'(t) T(t) r'(t) + 0 First find the derivative of r(t). r'(t) =(-3 sin(t),3 cos(t),0) (-3 sin(t), 3 cos(t), 0) Step 2 Now find the magnitude of r'(t). (-3 sin t)2 + (3 cos t)? + (0)2 9 sin? t + 9 cos² t = 3 3 Step 3 The unit tangent vector T(t) at t is as follows: (-3 sin t, 3 cos t, o) T(t) 1
Transcribed Image Text:Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P. 3 r(t) = (3 cos t, 3 sin t, 9), P(G 9) Step 1 The unit tangent vector T(t) att is defined as follows: r'(t) T(t) r'(t) + 0 First find the derivative of r(t). r'(t) =(-3 sin(t),3 cos(t),0) (-3 sin(t), 3 cos(t), 0) Step 2 Now find the magnitude of r'(t). (-3 sin t)2 + (3 cos t)? + (0)2 9 sin? t + 9 cos² t = 3 3 Step 3 The unit tangent vector T(t) at t is as follows: (-3 sin t, 3 cos t, o) T(t) 1
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