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Mathematics
Problem
Statement I If the vectors
a
\mathbf{a}
a
and
c
\mathbf{c}
c
are non-collinear then the lines
r
=
6
a
−
c
+
λ
(
2
c
−
a
)
\mathbf{r} = 6\mathbf{a} - \mathbf{c} + \lambda(2\mathbf{c} - \mathbf{a})
r
=
6
a
−
c
+
λ
(
2
c
−
a
)
and
r
=
a
−
c
+
μ
(
a
+
3
c
)
\mathbf{r} = \mathbf{a} - \mathbf{c} + \mu(\mathbf{a} + 3\mathbf{c})
r
=
a
−
c
+
μ
(
a
+
3
c
)
are coplanar. Statement II There exist
λ
\lambda
λ
and
μ
\mu
μ
such that the two values of
r
\mathbf{r}
r
in Statement I becomes same.
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