If \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0,\] where a, b and c are coplanar vectors, then for some scalar k [Roorkee 1985; RPET 1997]

\[\mathbf{a}+\mathbf{b}=k\,\mathbf{c}\]

\[\mathbf{a}+\mathbf{c}=k\,\mathbf{b}\]

\[\mathbf{b}+\mathbf{c}=k\,\mathbf{a}\]

If \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0,\] w

1.	If \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0,\] where a, b and c are coplanar vectors, then for some scalar k [Roorkee 1985; RPET 1997]
A.	\[\mathbf{a}+\mathbf{c}=k\,\mathbf{b}\]
B.	\[\mathbf{a}+\mathbf{b}=k\,\mathbf{c}\]
C.	\[\mathbf{b}+\mathbf{c}=k\,\mathbf{a}\]
D.	None of these
Answer» B. \[\mathbf{a}+\mathbf{b}=k\,\mathbf{c}\]

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If \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\ne 0,\] where a, b and c are coplanar vectors, then for some scalar k [Roorkee 1985; RPET 1997]

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