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Mathematics
Problem
Show that the points
P
(
a
+
2
b
+
c
)
P(\mathbf{a} + 2\mathbf{b} + \mathbf{c})
P
(
a
+
2
b
+
c
)
,
Q
(
a
−
b
−
c
)
Q(\mathbf{a} - \mathbf{b} - \mathbf{c})
Q
(
a
−
b
−
c
)
,
R
(
3
a
+
b
+
2
c
)
R(3\mathbf{a} + \mathbf{b} + 2\mathbf{c})
R
(
3
a
+
b
+
2
c
)
and
S
(
5
a
+
3
b
+
5
c
)
S(5\mathbf{a} + 3\mathbf{b} + 5\mathbf{c})
S
(
5
a
+
3
b
+
5
c
)
are coplanar given that
a
\mathbf{a}
a
,
b
\mathbf{b}
b
and
c
\mathbf{c}
c
are non-coplanar.
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