Answer:
Given \[\vec{A}\,.\,\vec{B}=\vec{B}\,.\,\vec{C}\] i.e. \[\text{AB
cos}{{\theta }_{\text{1}}}=\text{ BC cos}{{\theta }_{\text{2}}}\] ?.(i)
Where \[{{\theta }_{\text{1}}}\] is smaller angle between \[\vec{A}\]and\[\vec{B}\];
and \[{{\theta }_{\text{2}}}\] is the smaller abngle between \[\vec{B}\]and \[\vec{C}\].
From (i). \[\text{Acos}{{\theta }_{\text{1}}}=\text{C cos}{{\theta
}_{\text{2}}}\]
If \[{{\theta }_{\text{1}}}={{\theta }_{\text{2}}}\], then from
(ii), A = C or \[\vec{A}\,=\,\vec{C}\]
If \[{{\theta }_{\text{1}}}\ne {{\theta }_{\text{2}}}\], then
from (ii), A ¹ C or \[\vec{A}\,\ne \,\vec{C}\]
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