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A Triangular Plate

Let p⃗ is t...

Question

Let $\to p$ is the p.v of the orthocenter and $\to g$ is the p.v of the centroid of the triangle $A B C$ where circumcentre is the origin. If $\to p$ = $K \to g$ , then $K =$

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Solution

The correct option is A $3$
$U s e t h e c o n c e p t o f P o s i t i o n v e c t o r :$
$L e t O b e a f i x e d o r i g i n, t h e n p o s i t i o n v e c t o r o f P i s$
$C e n t r o i d i s i n t e r s e c t i o n o f \frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}$
$s o t h a t i n a t r i a n g l e A B C t h e o r t h o c e n t r e H, c e n t r o i d G a n d c i r c u m c e n t r e M a r e c o l l i n e a r a n d G d i v i d e s H M i n t e r n a l l y i n t h e r a t i o n 2 : 1$
$∴ g = \frac{2 \times M + 1 \times P}{3}$
$P = 3 g$
$∴ k = 3$

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