Find the unit tangent vector T(t) r(t)=5\cos t,\ 5\sin t,\ 4 P,\

hrostentsp6

hrostentsp6

Answered question

2021-12-05

To determine the unit tangent vector T(t) 
r(t)=5cost, 5sint, 4 
P, 52, 52, 4 find T(π4) and a set of parametric equations for the line tangent to the space curve at point p

Answer & Explanation

James Etheridge

James Etheridge

Beginner2021-12-06Added 16 answers

Step 1
r(t)=(5cos(t), 5sin(t), 4)
r(t)=(5sin(t), 5cos(t), 0)
||r(t)||=(5sin(t))2+(5cos(t))2+(0)2=5
Unit tangent vector is T(t)=r(t)||r(t)||
T(t)=(5sin(t), 5cos(t), 0)5=(sin(t), cos(t), 0)
At t=π4
T(π4)=(2{2}, 22, 0
The unit tangent vector T(t) at t=π4 is (22, 22, 0)
The point is P=(52, 52, 4)
Therefore, a set of parametric equations for the line tangent to the space curve at point P is
(52, 52, 4)+t(22, 22, 0)
=(5222t, 52+22t, 4)
Therefore

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