A) \[\overrightarrow{AC}\]
B) \[\frac{1}{2}\overrightarrow{AC}\]
C) \[\frac{2}{3}\overrightarrow{AC}\]
D) \[\frac{3}{2}\overrightarrow{AC}\]
Correct Answer: D
Solution :
\[\overrightarrow{AP}\,=\overrightarrow{AB}+\overrightarrow{BP}=\overrightarrow{AB}+\frac{1}{2}\overrightarrow{BC}=\overrightarrow{AB}+\frac{1}{2}\overrightarrow{AD}\] ?..(i) \[\overrightarrow{AQ}=\overrightarrow{AD}+\overrightarrow{DQ}=\overrightarrow{AD}+\frac{1}{2}\overrightarrow{DC}=\overrightarrow{AD}+\frac{1}{2}\overrightarrow{AB}\] ?..(ii) By (i) and (ii), we get, \[\overrightarrow{AP}+\overrightarrow{AQ}=\frac{3}{2}(\overrightarrow{AB}+\overrightarrow{AD})=\frac{3}{2}(\overrightarrow{AB}+\overrightarrow{BC})=\frac{3}{2}\overrightarrow{AC}\].You need to login to perform this action.
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