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The positions of rational numbers a, B and C on the number axis are shown in the figure. The simplified formula IAI Ia + bi + IC AI + IB CI graph: -- C -------- 0 --- a --- B --- →
According to the number axis
ca>0
a>0 -a
Simplify ia-bi-ic-ai + ib-ci-iai B ------- a --- 0 ------ C
From the meaning of the title:
|A-B|-|C-A|+|B-C|-|A|
=（A-B）-（C-A）+（C-B）-（-A）
=A-B-C+A+C-B+A
=3A-2B
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It is proved that if there is a real number s, t which is not all 0, such that SA + TB = 0, then a and B are collinear vectors; if a and B are not collinear, and SA + TB = 0, then s = t = o
SA + TB = 0 = - S / t a = B, let - S / T = k get a real number k that is not 0, such that K a = B, then a B is collinear (the definition of vector collinearity) x0d if a and B are not collinear, then there must not be a real number such that - S / t a = B, so t = 0, then SA + TB = 0, so sa = 0, because a is not 0, so s = 0, that is s = t = 0
What is the necessary and sufficient condition for a and B to be parallel
A * b = a * B
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