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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