# In triangle ABC (Fig 10.18),which of the following is not true :

(A) $\overrightarrow {AB}+\overrightarrow {BC} +\overrightarrow {CA}=0$

(B) $\overrightarrow {AB}+\overrightarrow {BC} -\overrightarrow {AC}=0$

(C) $\overrightarrow {AB}+\overrightarrow {BC} -\overrightarrow {CA}=0$

(D) $\overrightarrow {AB}-\overrightarrow {CB} +\overrightarrow {CA}=0$

Toolbox:
• Triangle law of addition states that in a triangle ABC, $\overrightarrow {AB}+\overrightarrow {BC} +\overrightarrow {CA}=0$
Step 1:
In a triangle ABC,according to triangle law of addition,$\overrightarrow {AB}+\overrightarrow {BC} +\overrightarrow {CA}=0$
Hence (A) is correct.
Step 2:
$\overrightarrow{CA}=-\overrightarrow{AC}$
Apply this in triangle law of addition $\overrightarrow {AB}+\overrightarrow {BC} +\overrightarrow {CA}=0$
Therefore $\overrightarrow {AB}+\overrightarrow {BC} -\overrightarrow {AC}=0$
Hence (B) is also correct.
Step 3:
$\overrightarrow{BC}=-\overrightarrow {CB}$
Apply this in triangle law of addition $\overrightarrow {AB}+\overrightarrow {BC} +\overrightarrow {CA}=0$
Therefore $\overrightarrow {AB}-\overrightarrow {CB} +\overrightarrow {CA}=0$
Hence (D) is also correct.
Step 4:
According to triangle law of addition $\overrightarrow {AB}+\overrightarrow {BC} +\overrightarrow {CA}=0$
Therefore $\overrightarrow {AB}+\overrightarrow {BC} -\overrightarrow {CA}=0$ is not true statement.
Hence (C) is not true.