Student[MultivariateCalculus][Angle]  Determine the angle between lines, vectors, and planes.

Calling Sequence


Angle(x, y)


Parameters


x



a vector, a line, or a plane

y



a vector, a line, or a plane





Description


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The Angle command determines the angle between two vectors, a vector and a line, a vector and a plane, two lines, a line and a plane, or two planes.



Notes


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The angle between two intersecting lines can be measured at the intersection point; the angle returned is in the interval . When two lines do not intersect, we define the angle determined by them as the angle between two lines through the origin parallel to the given lines.

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The angle between two planes is equal to the angle between their normals.

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The angle between a line and a plane is equal to the complement of the angle between the line and the normal of the plane.

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An angle involving one vector, v, is the same as if instead of the vector, you had supplied a line having v as its direction. An angle between two vectors is slightly different, in that it can attain all values in .



Compatibility


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The Student[MultivariateCalculus][Angle] command was introduced in Maple 18.



Examples


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Angle between two vectors
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 (1) 
Angle between a vector and a line
>


 (2) 
Angle between a vector and a plane
>


 (3) 
Angle between two lines
>


 (4) 
Angle between a line and a plane
>


 (5) 
Angle between two planes
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 (6) 


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