Decomposition of vectors.
Theorem 1. An arbitrary vector
in the plane can be decomposed into two noncollinear vectors:
.
Proof.Consider the parallelogram with sides parallel to the vectors 
and 
. We draw the vector 
from the point À and take the projections of its tail onto the lines containing and . By the summation rule, the vector is equal to
| |
,
Â
where 
and 
.
Substituting this expression, we obtain
, as required. Ñ