IIT JEE , AIEEE Forum - Mathematics , Vectors

mohile

if O be the circumcentre and O' be the orthocentre of a triangle ABC then vectorOA+vectorOB+vectorOC is equal to 3vectorOO' or 2OO' or OO' or O'O.

ramkumar_november

its OO' ..

mohile

your answer is correct.but will you please explain me how you got that answer.

ramkumar_november

please click and download the diagram for better view.....

$In\;\;\Delta AO$

$Triangles\;\;AGO$

$\frac{OG}{O$

$Therefore\;\;2.OG\;=\;O$

$OA+OB+OC\;=\;OA+(OB+OC)$

$OA+OB+OC\;=\;OA+2OD\;\;\;(D\;is \;midpoint\;of\;BC)$

$OA+OB+OC\;=\;(1+2).OG\;\;\;(G\;divides\;AD\;in\;the\;ratio\;2:1)$

$OA+OB+OC\;=\;3OG$

$OA+OB+OC\;=\;2OG+OG$

$OA+OB+OC\;=\;O$

$OA+OB+OC\;=\;OO$

hence proved......

here is the diagram.........