$\"\"$

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The vector equation is $\"\"$ at $\"\"$ .

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(a)

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Graph:

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Graph the vector $\"\"$ .

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$\"\"$

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$\"\"$

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(b)

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The vector is $\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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The tangent vector $\"\"$ at $\"\"$ .

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$\"\"$ .

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$\"\"$

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Therefore, $\"\"$ and $\"\"$ . $\"\"$

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(c)

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Graph the position vector $\"\"$ and the tangent vector $\"\"$ at $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Graph :

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Graph of the vectors $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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(a)

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Graph:

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Graph the vector $\"\"$ .

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$\"\"$

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(b) $\"\"$ .

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(c)

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Graph :

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Graph of the vectors $\"\"$ and $\"\"$ .

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$\"\"$ .