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 equal to _______

Question

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 equal to _______, 2 Q P →, 2 P Q →, P Q →, Q P →

MARKS App · Accepted Answer

Let P be origin. Now from the above triangle we can write P A → = a → , P A → = b → , P C → = c → . Also, we know that centroid G divides orthocentre Q and Circumcentre P in the ratio 2 : 1 . Now P G → = a → + b → + c → 3 ⇒ P Q → = 3 a → + b → + c → 3 ⇒ P Q → = a → + b → + c → = P A → + P B → + P C → Therefore, the required answer is P Q → .

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