In triangle $ABC$, which of the following is not true:
• $\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = \vec 0$
• $\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {AC} = \vec 0$
• $\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} = \vec 0$
• $\overrightarrow {AB} - \overrightarrow {CB} + \overrightarrow {CA} = \vec 0$
In triangle $ABC$, which of the following is not true:
• $\overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = \vec 0$
• $\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {AC} = \vec 0$
• $\overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} = \vec 0$
• $\overrightarrow {AB} - \overrightarrow {CB} + \overrightarrow {CA} = \vec 0$
Official Solution
{Option c is Correct}
By law of vectors, $\overrightarrow {AB} + \overrightarrow {BC} = \overrightarrow {AC}$
$\Rightarrow \overrightarrow {AB} + \overrightarrow {BC} = - \overrightarrow {CA}$
$\Rightarrow \overrightarrow {AB} + \overrightarrow {BC} + \overrightarrow {CA} = \vec 0 - \Rightarrow \overrightarrow {AB} + \overrightarrow {BC} - \overrightarrow {CA} \ne \vec 0$
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