and are the position vectors of points A, B and C respectively, prove that : is a vector perpendicular to the plane of triangle ABC.

if represents the sides AB,

if represent the sides BC,

if respresent the sidesAC of triangle ABC

is perpendicular to plane of triangle ABC. …… (i)

is perpendicular to plane of triangle ABC. …… (ii)

is perpendicular to plane of triangle ABC. …… (iii)

adding all the (i) + (ii) + (iii)

hence is a vector perpendicular to the plane of the triangle ABC