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Difference between revisions of "Co-planar vectors"

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Vectors that are parallel to one plane. A necessary and sufficient condition for the co-planarity of three vectors
 
Vectors that are parallel to one plane. A necessary and sufficient condition for the co-planarity of three vectors
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022710/c0227101.png" /></td> </tr></table>
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$$
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\mathbf a _ {1}  = \{ x _ {1} , y _ {1} , z _ {1} \} ,\ \
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\mathbf a _ {2}  = \{ x _ {2} , y _ {2} , z _ {2} \} ,\ \
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\mathbf a _ {3}  = \{ x _ {3} , y _ {3} , z _ {3} \}
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$$
  
 
is the equation
 
is the equation
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c022/c022710/c0227102.png" /></td> </tr></table>
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$$
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\left |
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\begin{array}{lll}
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x _ {1}  &y _ {1}  &z _ {1}  \\
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x _ {2}  &y _ {2}  &z _ {2}  \\
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x _ {3}  &y _ {3}  &z _ {3}  \\
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\end{array}
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\right |  = 0.
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$$

Latest revision as of 17:45, 4 June 2020


Vectors that are parallel to one plane. A necessary and sufficient condition for the co-planarity of three vectors

$$ \mathbf a _ {1} = \{ x _ {1} , y _ {1} , z _ {1} \} ,\ \ \mathbf a _ {2} = \{ x _ {2} , y _ {2} , z _ {2} \} ,\ \ \mathbf a _ {3} = \{ x _ {3} , y _ {3} , z _ {3} \} $$

is the equation

$$ \left | \begin{array}{lll} x _ {1} &y _ {1} &z _ {1} \\ x _ {2} &y _ {2} &z _ {2} \\ x _ {3} &y _ {3} &z _ {3} \\ \end{array} \right | = 0. $$

How to Cite This Entry:
Co-planar vectors. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Co-planar_vectors&oldid=46370