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Question:
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In triangle $\mathbf{A B C}$ (fig.), which of the following is not true:
(a) $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}=\overrightarrow{0}$
(b) $\overrightarrow{A B}+\overrightarrow{B C}-\overrightarrow{A C}=\overrightarrow{0}$
(c) $\overrightarrow{A B}+\overrightarrow{B C}-\overrightarrow{C A}=\overrightarrow{0}$
(d) $\overrightarrow{A B}-\overrightarrow{C B}+\overrightarrow{C A}=\overrightarrow{0}$
(a) $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}=\overrightarrow{0}$
(b) $\overrightarrow{A B}+\overrightarrow{B C}-\overrightarrow{A C}=\overrightarrow{0}$
(c) $\overrightarrow{A B}+\overrightarrow{B C}-\overrightarrow{C A}=\overrightarrow{0}$
(d) $\overrightarrow{A B}-\overrightarrow{C B}+\overrightarrow{C A}=\overrightarrow{0}$
Solution:
1574 Upvotes
Verified Answer
We know that
$$
\begin{aligned}
\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A} &=\overrightarrow{0} \\
\Rightarrow \quad \overline{A B}+\overrightarrow{B C}-\overrightarrow{A C} &=\overrightarrow{0}
\end{aligned}
$$
Hence option (c) is not correct.
$$
\begin{aligned}
\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A} &=\overrightarrow{0} \\
\Rightarrow \quad \overline{A B}+\overrightarrow{B C}-\overrightarrow{A C} &=\overrightarrow{0}
\end{aligned}
$$
Hence option (c) is not correct.
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