Question

Problem Code: 1443 The vector function $r(t) = \sin(t^3)\mathbf{i} - 2\cos(t^3)\mathbf{j} + \sqrt{3}\sin(t^3)\mathbf{k}$ determines a curve C in space. Assume $t > 0$. a. [4 points] Find the unit tangent vector $T(t)$. b. [3 points] Find the principal normal vector $N(t)$. c. [2 points] Find the curvature, $\kappa$. d. [4 points] Find the tangential and normal components of acceleration and express the acceleration vector, $a(t)$, in terms of the unit tangent vector T and the principal normal vector N.

          Problem Code: 1443
The vector function $r(t) = \sin(t^3)\mathbf{i} - 2\cos(t^3)\mathbf{j} + \sqrt{3}\sin(t^3)\mathbf{k}$ determines a curve C in space.
Assume $t > 0$.
a. [4 points] Find the unit tangent vector $T(t)$.
b. [3 points] Find the principal normal vector $N(t)$.
c. [2 points] Find the curvature, $\kappa$.
d. [4 points] Find the tangential and normal components of acceleration and express the acceleration vector, $a(t)$, in terms of the unit tangent vector T and the principal normal vector N.

Problem Code: 1443
The vector function r(t) = sin(t^3)𝐢 - 2cos(t^3)𝐣 + √(3)sin(t^3)𝐤 determines a curve C in space.
Assume t > 0.
a. [4 points] Find the unit tangent vector T(t).
b. [3 points] Find the principal normal vector N(t).
c. [2 points] Find the curvature, κ.
d. [4 points] Find the tangential and normal components of acceleration and express the acceleration vector, a(t), in terms of the unit tangent vector T and the principal normal vector N.

Added by Veronica I.

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