# Prove using vectors two lines bisect each other

I have the points $$O, A, B$$ and $$C$$.

Relative to $$O$$, the position vectors of $$A$$, $$B$$ and $$C$$ are $$(1,4, 2 )$$, $$(3, 3, 3)$$, $$( 2, -1, 1)$$

Want to show that the lines $$OB$$ and $$AC$$ bisect each other.

Is it sufficient to show that $$\frac{1}{2} \vec{OB} = \vec{OA} + \frac{1}{2} \vec{AC}$$?

Are there other ways using vectors?

• If the diagonals of a quadrilateral bisect each other, it is a parallelogram. So, B=A+C. – Anubhab Ghosal Apr 12 at 15:37

You may also show that $$\vec{OA} = \vec{CB}$$ and $$\vec{OC} = \vec{AB}$$ which make the quadrilateral OABC into a parallelogram where the diagonals bisect each other.