Vector Calculus

Cover Vector Calculus
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Fr x dr=C. NS, where S stands for the area enclosed by the curve and n a unit vector along the normal to the plane of the curve.
The ratio- f(r). Dr=C. N does not then depend on the parti- S cular curve round which we integrate, but it depends on the orientation of the plane of the curve, on the vector n. This ratio obviously again attains its maximum value when n is taken in the direction of C. The vector constant of <(/) then is a vector in the direction of the normal to that plane, round
...any curve on which if we calculate the line integral of <(r) the ratio of this integral to the area of the curve is maximum, and the magnitude of the vector constant is equal to this maximum ratio.
21. There is just one bit of work more in connection with linear vector functions before we are ready for the Differential Calculus of vector functions.
If a is any constant vector, a x (/) is of course also a linear vector function of r. We proceed to find D 1 and C l the scalar and vector constants of a x

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