KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 84 of 120

Marks: +1, -0

Let ABC be an acute scalene triangle, and O and H be its circumcentre and orthocenter respectively. Further let N be the midpoint of OH. The value of the vector sum

{NA}↖{→}+ {NB}↖{→}+ {NC}↖{→}

$0↖{→}$ (zero vector)
${HO }↖{→}$
$1/2 {HO }↖{→}$
$1/2{ OH}↖{→}$

Validate

Solution:

Circumcenter (origin O)

(O )↖{→}=({{a↖{→}+b↖{→}+c↖{→}}/3);H=({{a↖{→}+b↖{→}+c↖{→}}/2)

N ↖{→}=1/4({a↖{→}+b↖{→}+c↖{→})

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