Difference between revisions of "Co-planar vectors"
From Encyclopedia of Mathematics
(Importing text file) |
Ulf Rehmann (talk | contribs) m (tex encoded by computer) |
||
Line 1: | Line 1: | ||
+ | <!-- | ||
+ | c0227101.png | ||
+ | $#A+1 = 2 n = 0 | ||
+ | $#C+1 = 2 : ~/encyclopedia/old_files/data/C022/C.0202710 Co\AAhplanar vectors | ||
+ | Automatically converted into TeX, above some diagnostics. | ||
+ | Please remove this comment and the {{TEX|auto}} line below, | ||
+ | if TeX found to be correct. | ||
+ | --> | ||
+ | |||
+ | {{TEX|auto}} | ||
+ | {{TEX|done}} | ||
+ | |||
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 | ||
− | + | $$ | |
+ | \mathbf a _ {1} = \{ x _ {1} , y _ {1} , z _ {1} \} ,\ \ | ||
+ | \mathbf a _ {2} = \{ x _ {2} , y _ {2} , z _ {2} \} ,\ \ | ||
+ | \mathbf a _ {3} = \{ x _ {3} , y _ {3} , z _ {3} \} | ||
+ | $$ | ||
is the equation | is the equation | ||
− | + | $$ | |
+ | \left | | ||
+ | \begin{array}{lll} | ||
+ | x _ {1} &y _ {1} &z _ {1} \\ | ||
+ | x _ {2} &y _ {2} &z _ {2} \\ | ||
+ | x _ {3} &y _ {3} &z _ {3} \\ | ||
+ | \end{array} | ||
+ | \right | = 0. | ||
+ | $$ |
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
Co-planar vectors. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Co-planar_vectors&oldid=46370