If the points P and Q are respectively the circumcenter and the orthocentre of a A B C , then P A + P B + P C is [2023]

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Solution

Q.
If the points P and Q are respectively the circumcenter and the orthocentre of a $∆ A B C$ , then $\vec{P A} + \vec{P B} + \vec{P C}$ is [2023]

1 $2 \vec{P Q}$

2 $\vec{Q P}$

3 $2 \vec{Q P}$

4 $\vec{P Q}$

Ans.
(4)

$\vec{P A} + \vec{P B} + \vec{P C} = \vec{a} + \vec{b} + \vec{c}$

$= \frac{3 (\vec{a} + \vec{b} + \vec{c})}{3}$

$= 3 \vec{P G} = \vec{P Q}$

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