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Question
In Figure, which of the following is not true?
Options
\[\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} = \vec{0}\]
\[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{AC} = \vec{0}\]
\[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{CA} = \vec{0}\]
\[\overrightarrow{AB} - \overrightarrow{CB} + \overrightarrow{CA} = \vec{0}\]
Solution
\[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{CA} = \vec{0}\]
We have, LHS = \[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{CA} = \overrightarrow{AC} - \overrightarrow{CA}\] [∵ \[\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}\]
\[= - \overrightarrow{CA} - \overrightarrow{CA} \]
\[ = - 2 \overrightarrow{CA}\]
So, LHS \[\neq\] RHS
Hence, It is not true.
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