Fundamental theorems of vectors:
Fundamental theorem of vectors in two-dimensions
If and be 2 non-zero non-collinear vectors, then the vector in the plane of and can be expressed uniquely as a linear combination of and that is there exist unique l, mÎR such that l +m = .
This means that if l1 + m1 = l2 + m2 then l1 = l2 and m1 = m2.
Fundamental theorem of vectors in three-dimensions
If , and be 3 non-zero, non-coplanar vectors in space, then any vector in space can be expressed uniquely as linear combination of , and .
That is there exist unique l, m, n ÎR such that l + m + n =
This means that if l1 + m1+ n1 = l2+ m2+ n2, then l1 = l2, m1 = m2 and n1 = n2.
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