nowafterobservingthesesvectorsweconcludethat,theseareequationsinstraightlines. In three dimensional space the cosets of a line (plane) through the origin is the set of all lines (planes) parallel to it.
If we consider the equation a=−b−2cwherebandcarefreevariables.
just replacing b and c values, keeping a constant, we get different solutions and all these solutions are gives parallel lines to each other. So all these are cosets of the given line 2a+2b+4c=0 in R3.
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