Let P be a point interior to the acute triangle A B C. If P A+P B+P C is a null vector, then w.r.t. triangle A B C point P is its

Question

Let P be a point interior to the acute triangle A B C. If P A+P B+P C is a null vector, then w.r.t. triangle A B C point P is its (A) centroid (B) orthocentre (C) incentre (D) circumcentre

Tardigrade Admin · Accepted Answer

veca- vecp+ vecb- vecp+ vecc- vecp=0 or vecp=( veca+ vecb+ vecc/3) Hence, P is centroid.

Q. Let $P$ be a point interior to the acute triangle $A BC$ . If $P A + PB + PC$ is a null vector, then w.r.t. triangle $A BC$ point $P$ is its

centroid

orthocentre

incentre

circumcentre

$a - p + b - p + c - p = 0$
or $p = \frac{a + b + c}{3}$
Hence, $P$ is centroid.

Q. Let P be a point interior to the acute triangle ABC. If PA+PB+PC is a null vector, then w.r.t. triangle ABC point P is its