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Mathematics
Mathematics
Problem
If
a
\mathbf{a}
a
,
b
\mathbf{b}
b
and
c
\mathbf{c}
c
are position vectors of the vertices
A
A
A
,
B
B
B
and
C
C
C
of
△
A
B
C
\triangle ABC
△
A
B
C
, show that the area of
△
A
B
C
\triangle ABC
△
A
B
C
is
1
2
∣
a
×
b
+
b
×
c
+
c
×
a
∣
\frac{1}{2} |\mathbf{a} \times \mathbf{b} + \mathbf{b} \times \mathbf{c} + \mathbf{c} \times \mathbf{a}|
2
1
∣
a
×
b
+
b
×
c
+
c
×
a
∣
. Deduce the condition for points
a
\mathbf{a}
a
,
b
\mathbf{b}
b
and
c
\mathbf{c}
c
to be collinear.
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