If `veca, vecb, vecc` are the position vectors of the vertices of an equilateral triangle whose orthocenter is at the origin, then

Options

A. `vec(a)+vec(a)+vec(c)=vec(0)`
B. `vec(a)+vec(b)+vec(c)`= unit vector
C. `vec(a)+vec(b)=vec(c)`
D. `vec(a)=vec(b)+vec(c)`

Answer

A

Explanation

Position vectors of vertices A, B andC are `vec(a), vec(b) and vec(c)`.

`:'` triangle is equilateral.
`:.` Centroid and orthocenter will coincide.
Centroid `-=` orthocenter position vector
`=(1)/(3) (vec(a)+vec(b)+vec(c))`
`:'` given in question orthocenter is at origin.
Hence `(1)/(3)(vec(a)++vec(b)+vec(c))=0`
`vec(a)+vec(b)+vec(c)=0`