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Problem
Problem
If
a
×
b
=
b
×
c
≠
0
\mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} \neq \mathbf{0}
a
×
b
=
b
×
c
=
0
with
a
≠
−
c
\mathbf{a} \neq -\mathbf{c}
a
=
−
c
then show that
a
+
c
=
k
b
\mathbf{a} + \mathbf{c} = k\mathbf{b}
a
+
c
=
k
b
, where
k
k
k
is scalar.
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