Vectors

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24 May 2010 11:00:10 IST
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what is a coplanar vector
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Vectors

what is a coplanar vector



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Cool goIITian

Joined: 29 Oct 2009
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24 May 2010 11:01:34 IST
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 Vectors in the same plane are called co-planar vectors.


Blazing goIITian

Joined: 22 May 2009
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31 Jan 2011 15:43:37 IST
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hi

Geometric objects lying in a common plane are said to be coplanar. Three noncollinear points determine a plane and so are trivially coplanar. Four points are coplanar iff the volume of the tetrahedron defined by them is 0,

 |x_1 y_1 z_1 1; x_2 y_2 z_2 1; x_3 y_3 z_3 1; x_4 y_4 z_4 1|=0.

Coplanarity is equivalent to the statement that the pair of lines determined by the four points are not skew, and can be equivalently stated in vector form as

 (x_3-x_1)·[(x_2-x_1)x(x_4-x_3)]=0.

An arbitrary number of n points x_1, ..., x_n can be tested for coplanarity by finding the point-plane distances of the points x_4, ..., x_n from the plane determined by (x_1,x_2,x_3) and checking if they are all zero. If so, the points are all coplanar.

A set of n vectors V is coplanar if the nullity of the linear mapping defined by V has dimension 1, the matrix rank of V (or equivalently, the number of its singular values) is n-1 (Abbott 2004).

Parallel lines in three-dimensional space are coplanar, but skew lines are not  !!!!


New kid on the Block

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14 May 2012 11:56:33 IST
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what is a coplanar vector and number of coplanar vector having different magnititudes added up to zero resultant.

Cool goIITian

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14 May 2012 12:40:28 IST
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New kid on the Block

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14 May 2012 12:43:42 IST
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what is a coplanar vector



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