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Coplanar vectors 
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#1
Aug2812, 01:24 PM

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Two free vectors are always coplanar.
Then if A and B are free vectors, are A, B, and A+B all coplanar in all cases? 


#2
Aug2812, 01:53 PM

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Any two vectors that start from the same point (you can assume that they start from the origin) determine a plane. Any linear combination of these vectors (including 1*A + 1*B) also lies in that same plane. 


#3
Aug2812, 02:11 PM

P: 1,304

Cool.
How about this: If two vectors are linearly dependent, they are collinear. They are always coplanar. If three vectors are linearly dependent, they are coplanar. Three vectors are always all co"cubeular" (I don't know a word like coplanar for a three dimensional object.) Based on this pattern, it correct to say that: If n vectors are linearly dependent, then they are co(n1 space object) and are always co(n space object). Since for two vectors, an n1 space object is a line, for three it is a plane, and so on. Am I making sense? 


#4
Aug2812, 04:10 PM

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P: 21,397

Coplanar vectors



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