In a triangle ABC, E and F are the feets of the perpendiculars from B and C to AC and AB respectively. DE and CF meet at H. Let(HA) ⃗=x, (HB) ⃗=y, and (HC) ⃗=z.

I. Find(AB) ⃗, (AC) ⃗ and (BC) ⃗ in terms of x, y and z.
ii. Using the fact that BE is perpendicular to AC, obtain a relation between x, y and z.
iii. Obtain another relation between x, y and z using that CF and AB are perpendicular.

The first step of any geometry problem is to draw a diagram from the given information.

If you have not done that critical first step, it's time to do it now.

Also,
1. point D has not been defined in this post. Is D on BC such that AD is perpendicular to BC?
2. would "DE and CF meet at H." read "DA and CF meet at H.", i.e. is H the orthocentre?
3. what is Find(AB) ⃗..., would that mean (AB²)?