13.1: Space Curves

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Calc III Midterm 1

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6 Terms

1

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Line

r(t) = r_o + tv = <x_o+at, y_o+bt, z_o+ct>

<p><strong>r</strong>(t) = <strong>r</strong><sub>o</sub> + t<strong>v</strong> = <x<sub>o</sub>+at, y<sub>o</sub>+bt, z<sub>o</sub>+ct></p>

2

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Circle (2D: XY Plane)

r(t) = <cost, sint, 0>

<p><strong>r</strong>(t) = <cost, sint, 0></p>

3

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Circle (3D Space)

r(t) = <acost , asint, c>

<p><strong>r</strong>(t) = <acost , asint, c></p>

4

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Helix

r(t) = <cost, sint, t>

<p><strong>r</strong>(t) = <cost, sint, t></p>

5

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Parabola

r(t) = <t, t², 0>

<p>r(t) = <t, t<sup>2</sup>, 0></p>

6

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Helix (Shape)

Spiral around an axis

<p>Spiral around an axis</p>