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In a triangle...

Question

In a triangle $A B C,$ which of the following is not true:

- - \to A B + - - \to B C + - - \to C A = \to 0

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- - \to A B + - - \to B C - - - \to A C = \to 0

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- - \to A B + - - \to B C - - - \to C A = \to 0

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- - \to A B - - - \to C B + - - \to C A = \to 0

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Solution

The correct option is C $- - \to A B + - - \to B C - - - \to C A = \to 0$
By triangle law of vector addition $- - \to A B + - - \to B C = - - \to A C$
$\Rightarrow - - \to A B + - - \to B C = - - - \to C A$
$\Rightarrow - - \to A B + - - \to B C + - - \to C A = \to 0$

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