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Mathematics
Problem
If
a
,
b
\boldsymbol{a}, \boldsymbol{b}
a
,
b
and
c
\boldsymbol{c}
c
are non-coplanar vectors, then prove that the four points
2
a
+
3
b
−
c
,
a
−
2
b
+
3
c
,
3
a
+
4
b
−
2
c
2 \boldsymbol{a} + 3 \boldsymbol{b} - \boldsymbol{c}, \boldsymbol{a} - 2 \boldsymbol{b} + 3 \boldsymbol{c}, 3 \boldsymbol{a} + 4 \boldsymbol{b} - 2 \boldsymbol{c}
2
a
+
3
b
−
c
,
a
−
2
b
+
3
c
,
3
a
+
4
b
−
2
c
and
a
−
6
b
+
6
c
\boldsymbol{a} - 6 \boldsymbol{b} + 6 \boldsymbol{c}
a
−
6
b
+
6
c
are coplanar.
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