Vector Algebra Question 253
Question: If C is the middle point of AB and P is any point outside AB, then
[MNR 1991; UPSEAT 2000; AIEEE 2005]
Options:
A) $ \overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC} $
B) $ \overrightarrow{PA}+\overrightarrow{PB}=2,\overrightarrow{PC} $
C) $ \overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0 $
D) $ \overrightarrow{PA}+\overrightarrow{PB}+2,\overrightarrow{PC}=0 $
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Answer:
Correct Answer: B
Solution:
- $ \overrightarrow{PA}+\overrightarrow{PB}=(\overrightarrow{PA}+\overrightarrow{AC})+(\overrightarrow{PB}+\overrightarrow{BC})-(\overrightarrow{AC}+\overrightarrow{BC}) $ = $ \overrightarrow{PC}+\overrightarrow{PC}-(\overrightarrow{AC}-\overrightarrow{CB})=2\overrightarrow{PC}-0, $ $ (\because ,\overrightarrow{AC}=\overrightarrow{CB}) $
$ \therefore $ $ \overrightarrow{PA}+\overrightarrow{PB}=2\overrightarrow{PC} $ .
BETA
