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Mathematics
Problem
Given three vectors
a
\mathbf{a}
a
,
b
\mathbf{b}
b
,
c
\mathbf{c}
c
such that they are non-zero, non-coplanar vectors, then which of the following are coplanar. a.
a
+
b
\mathbf{a} + \mathbf{b}
a
+
b
,
b
+
c
\mathbf{b} + \mathbf{c}
b
+
c
,
c
+
a
\mathbf{c} + \mathbf{a}
c
+
a
b.
a
−
b
\mathbf{a} - \mathbf{b}
a
−
b
,
b
+
c
\mathbf{b} + \mathbf{c}
b
+
c
,
c
+
a
\mathbf{c} + \mathbf{a}
c
+
a
c.
a
+
b
\mathbf{a} + \mathbf{b}
a
+
b
,
b
−
c
\mathbf{b} - \mathbf{c}
b
−
c
,
c
+
a
\mathbf{c} + \mathbf{a}
c
+
a
d.
a
+
b
\mathbf{a} + \mathbf{b}
a
+
b
,
b
+
c
\mathbf{b} + \mathbf{c}
b
+
c
,
c
−
a
\mathbf{c} - \mathbf{a}
c
−
a
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