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191:, which can be made to coincide by translation to pass through a common point. The direction of a non-oriented line in a two-dimensional plane, given a Cartesian coordinate system, can be represented numerically by its
180:(ignoring or normalizing the radial component). A three-dimensional direction can be represented using a polar angle relative to a fixed polar axis and an azimuthal angle about the polar axis: the angular components of
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of the angles) between the given direction and the directions of the axes; the direction cosines are the coordinates of the associated unit vector.
269:) if they can be brought to lie on the same straight line without rotations; parallel directions are either codirectional or opposite.
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between the sphere and a ray in that direction emanating from the sphere's center; the tips of unit vectors emanating from a common
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Non-oriented straight lines can also be considered to have a direction, the common characteristic of all
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to share a common endpoint; equivalently, it is the common characteristic of
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are used as synonyms of codirectional and opposite, respectively.
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is defined in terms of several oriented reference lines, called
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A two-dimensional direction can also be represented by its
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A direction is used to represent linear objects such as
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Two vectors sharing the same direction are said to be
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between a pair of points) which can be made equal by
373:Handbook of mathematics and computational science
93:. Two codirectional vectors are not necessarily
101:sharing the same size (length) are said to be
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34:Three line segments with the same direction
251:if the unit vectors representing them are
370:Harris, John W.; Stöcker, Horst (1998).
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122:A direction is often represented as a
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27:Property shared by codirectional lines
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202:Examples of two 2D direction vectors
239:parallel (and opposite) directions
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376:. Birkhäuser. Chapter 6, p. 332.
288:(greater than a right angle) or
284:if they form, respectively, an
245:Two directions are said to be
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155:Cartesian coordinate system
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228:axis–angle representation
99:directional line segments
310:Body relative direction
404:Elementary mathematics
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182:spherical coordinates
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58:which coincide when
272:Two directions are
409:Euclidean geometry
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74:(by some positive
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18:Relative direction
320:Tangent direction
298:scalar projection
253:additive inverses
237:Two airplanes in
178:polar coordinates
163:direction cosines
146:point lie on the
76:scalar multiplier
68:relative position
48:spatial direction
16:(Redirected from
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315:Euclidean vector
208:axes of rotation
52:vector direction
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212:normal vectors
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338:Sometimes,
290:acute angle
220:orientation
165:(a list of
148:unit sphere
124:unit vector
117:free vector
104:equipollent
398:Categories
354:References
60:translated
257:antipodal
109:positions
44:direction
340:parallel
304:See also
262:parallel
248:opposite
97:. All co
95:colinear
40:geometry
265:(as in
226:(e.g.,
167:cosines
72:scaling
64:vectors
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275:obtuse
216:object
144:origin
138:, the
136:sphere
132:circle
326:Notes
281:acute
193:slope
174:angle
130:on a
128:point
378:ISBN
342:and
296:(or
210:and
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78:).
56:rays
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278:or
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222:in
218:'s
134:or
87:or
50:or
38:In
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362:^
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153:A
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