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Homework Help: What do you mean by direction cosine

  1. Mar 6, 2006 #1
    what do you mean by "direction cosine"

    i've just came through this term, and may someone please help clarify what does it mean?

  2. jcsd
  3. Mar 6, 2006 #2


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    If you project a unit vector down on your chosen set of axes, then the direction cosines are the length of the projection along each respective axis.
  4. Mar 6, 2006 #3


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    If a vector, v, in 2 dimensions, makes angle [itex]\theta_x[/itex] with the x-axis, then cos([itex]\theta_x[/itex])i+ sin([itex]\theta_x[/itex])j is a unit vector in the same direction as v. If [itex]\theta_y[/itex] is the angle that vector makes with the y axis, then [itex]\theta_y= \frac{\pi}{2}- \theta_x[/itex]) so sin([itex]\theta_x[/itex])= cos([itex]\theta_y[/itex] and that unit vector is cos([itex]\theta_x[/itex])i+ cos([itex]\theta_y[/itex])j.

    Similarly, if a vector, v, in 3 dimensions, make angle [itex]\theta_x[/itex] with the x-axis, angle [itex]\theta_y[/itex] with the y axis, and angle [itex]\theta_z[/itex] with the z-axis then a unit vector in the direction of v is cos([itex]\theta_x[/itex])i+ cos([itex]\theta_y[/itex])j+ cos([itex]\theta_z[/itex])k.

    Those are the "direction cosines" of the vector or line in the direction of the vector. Equivalently, if v is a unit vector in a given direction, its components are the direction cosines for that direction- its components are the cosine of the angle it makes with the corresponding axis.
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