Find the unit normal vector to the curve r(t) = \langle a\cos t, a\sin t, bt\rangle , where ...

Question:

Find the unit normal vector to the curve {eq}\mathbf r(t) = \langle a\cos t, a\sin t, bt\rangle {/eq}, where {eq}a \gt 0, b\gt 0 {/eq}

Unit Normal Vector:

The unit vector normal to a curve specified by the parametric equations

{eq}r(t) = x(t)\mathbf i + y(t)\mathbf j +z(t)\mathbf k {/eq}

is given by

{eq}\mathbf N(t) = \frac{ x''(t)\mathbf i + y''(t)\mathbf j +z''(t)\mathbf k } { \left \| x''(t)\mathbf i + y''(t)\mathbf j +z''(t)\mathbf k \right \|} {/eq}

where " is the second derivative and {eq}\left \| \right \| {/eq} is the norm operation.

Answer and Explanation:

We are given the curve:

{eq}\mathbf r(t) = \langle a\cos t, a\sin t, bt\rangle {/eq}, where {eq}a \gt 0, b\gt 0 {/eq}

By applying above definition...

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How to Do Vector Operations Using Components

from UExcel Physics: Study Guide & Test Prep

Chapter 2 / Lesson 7
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