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(A) The magnitude of the resultant vector $\overrightarrow C = \overrightarrow A + \overrightarrow B$ is given by $|\overrightarrow C| = \sqrt{|\overr

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$A$ and $C$

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(A) The magnitude of the resultant vector $\overrightarrow C = \overrightarrow A + \overrightarrow B$ is given by $|\overrightarrow C| = \sqrt{|\overrightarrow A|^2 + |\overrightarrow B|^2 + 2|\overrightarrow A||\overrightarrow B| \cos 	heta}$,where $	heta$ is the angle between $\overrightarrow A$ and $\overrightarrow B$.Statement $(A)$: If $\overrightarrow A$ and $\overrightarrow B$ are vectors such that their sum $\overrightarrow C$ has a smaller magnitude than both,it is possible if the angle between them is obtuse (specifically,$90^\circ Statement $(B)$: This is incorrect because if $\overrightarrow B$ is a null vector or if the angle $	heta$ is such that the resultant magnitude decreases,$|\overrightarrow C|$ can be less than or equal to $|\overrightarrow A|$.Statement $(C)$: If $\overrightarrow A$ and $\overrightarrow B$ are in the same direction $(	heta = 0^\circ)$,then $|\overrightarrow C| = |\overrightarrow A| + |\overrightarrow B|$. Thus,$(C)$ is correct.Statement $(D)$: This is the negation of $(C)$ and is therefore incorrect.Since $(A)$ and $(C)$ are correct,the correct option is $A$.

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