278
Question
If c is the middle point of AB and P is any point outside AB then
If c is the middle point of AB and P is any point outside AB then
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Solution
The correct option is B −−→PA+−−→PB=2−−→PC
−−→AC and −−→BC
have equal magnitude and opposite direction
Therefore both are negative vectors of each other
∴−−→AC+−−→BC=0
In △PAC we have
−−→PA+−−→AC=−−→PC ...(1)
In △PBC, we have
−−→PB+−−→BC=−−→PC ...(2)
From (1) and (2)
−−→PA+−−→PB+(−−→AC+−−→BC)=2−−→PC⇒−−→PA+−−→PB=2−−→PC
−−→AC and −−→BC
have equal magnitude and opposite direction
Therefore both are negative vectors of each other
∴−−→AC+−−→BC=0
In △PAC we have
−−→PA+−−→AC=−−→PC ...(1)
In △PBC, we have
−−→PB+−−→BC=−−→PC ...(2)
From (1) and (2)
−−→PA+−−→PB+(−−→AC+−−→BC)=2−−→PC⇒−−→PA+−−→PB=2−−→PC
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