| 21. | As an example suppose X is a timelike tangent vector with respect to the \, g metric.
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| 22. | Thus the length of a tangent vector cannot be defined, but the angle between two vectors still can.
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| 23. | Is a tangent vector to " C " in curvilinear coordinates ( using the chain rule ).
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| 24. | In modern terminology virtual displacement is a tangent vector to the manifold representing the constraints at a fixed time.
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| 25. | There is an associated notion of Carath�odory length for tangent vectors to the ball " B ".
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| 26. | More strictly this defines an affine tangent space, distinct from the space of tangent vectors described by modern terminology.
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| 27. | To get the angle, we need the tangent vectors and at along the directions of sides and, respectively.
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| 28. | Therefore, all tangent vectors in a point p span a linear space, called the tangent space at point p.
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| 29. | This means that the directional derivative depends only on the tangent vector of the curve at " p ".
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| 30. | Though, for a curve whose tangent vectors all have the same sign of magnitude, the arc length is defined.
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