Ask Question
12 February, 02:25

Consider the vector function given below.

r (t) = (3t^2, sin (t) - tcos (t), cos (t) + tsin (t)), t>0

Do the following

(a) Find the unit tangent and unit normal vectors T (t) and N (t)

T (t) =

N (t) =

(b) Find the curvature

k (t) =

+5
Answers (1)
  1. 12 February, 06:20
    0
    The tangent vector is by definition the derivative of r (t) with respect to t:

    T' = dr/dt =

    The unit vector T = T'/|T'| = / sqrt (36t^2 + t^tsin (t) ^2 + t^2cos (t^2))

    T = / (t*sqrt (37)) = / sqrt (37)

    Now the normal unit vector N is perpendicular to r/|r| and T. It is the second derivative of r/|r| with repsect to time

    N' = d^2r/dt^2 =

    N = N'/|N'| = / sqrt (36 + sin^2t + 2tsin (t) cos (t) + t^2cos^2t + cos^2 (t) - 2tcos (t) sin (t) + t^2sin^2t)

    N = / sqrt (37 + t^2)
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Consider the vector function given below. r (t) = (3t^2, sin (t) - tcos (t), cos (t) + tsin (t)), t>0 Do the following (a) Find the unit ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers