Chapter 9: Vector Calculus
Section 9.2: Vector Objects
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Examples
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Example 9.2.1
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Enter the Cartesian point as a free vector, then change to polar coordinates.
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Example 9.2.2
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Enter as the PositionVector the parametrically-defined curve , , .
Graph the curve, and at , include unit tangent and principal normal vectors, and members of the field .
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Example 9.2.3
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Enter as the PositionVector the parametrically-defined curve , , .
Graph the curve, and at , include members of the vector field .
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Example 9.2.4
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Draw the surface , and on it, the coordinate curves and . Along these coordinate curves, draw tangent, principal normal, and binormal vectors.
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Example 9.2.5
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Draw the surface , and on it, from the vector field , normalized vectors and their normal components, at the points corresponding to and .
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Example 9.2.6
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The vertices of a triangle are A:, B:, C:. Draw the triangle with sides as vectors from A to B, B to C, and C to A.
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Example 9.2.7
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At the point , evaluate the vector field and the free vector V whose components are the same as those of F. On the same set of axes, draw both resulting vectors.
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Example 9.2.8
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Express in polar coordinates the Cartesian vector field , where and are constants.
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Example 9.2.9
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Express in polar coordinates the Cartesian vector field .
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Example 9.2.10
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Express in polar coordinates the Cartesian vector field .
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Example 9.2.11
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Express in spherical coordinates the Cartesian vector field , where are constants.
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Example 9.2.12
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Draw the constant Cartesian vector field , then express F in polar coordinates and draw that field.
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Example 9.2.13
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Express in Cartesian coordinates the polar vector field whose components are the constants and .
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Example 9.2.14
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Express in Cartesian coordinates the spherical vector field whose components are the constants , , and .
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