WHY ordered? Because (2,3,5) and (5,3,2) are different points. The position in the triple tells you which ruler.
HOW we draw it (right-handed system): Point the fingers of your right hand along +x, curl them towards +y; your thumb points along +z. Mathematics uses this convention everywhere (cross products, etc.).
Imagine the corner of your bedroom. The floor and two walls meet at that corner — that's "zero, zero, zero". To tell a friend where a balloon is floating, you say: "go 2 metres along this wall, 3 metres along that wall, and 4 metres up." Those three numbers (2,3,4) are the balloon's address. The walls and floor cut the whole room (and the space outside it too) into 8 boxes — those are the octants, like 8 invisible rooms meeting at one corner.
Dekho, 2D mein hum kisi point ko sirf do numbers se bataate hain — (x,y), yaani left-right aur up-down. Lekin asli duniya mein depth bhi hoti hai, isliye 3D mein ek teesra perpendicular axis add karte hain: z-axis. Toh ab har point ka address teen numbers ka hota hai — (x,y,z). Yeh ordered triple hai, matlab order important hai: (2,3,5) aur (5,3,2) ek hi point nahi hain.
Apne room ke corner ko socho — floor aur do walls jahan milte hain, wahi origin hai. Floor = xy-plane (z=0), aur do walls = yz-plane (x=0) aur zx-plane (y=0). In teen planes ne poore space ko kaat ke 8 boxes bana diye — inhe octants kehte hain. 8 kyun? Kyunki x, y, z har ek plus ya minus ho sakta hai, toh 2×2×2=8. Yaad rakho: 2D mein 4 quadrants the, 3D mein doosra axis add hone se double ho gaye.
Sign dekhke octant pehchaano: (+,+,+) Octant I, (−,−,−) Octant VII, waghairah. Aur ek simple rule: agar ek coordinate zero hai toh point kisi plane mein hai; do zero hain toh axis par; teeno zero hain toh origin.
Distance ka formula bhi ratna mat — derive karo. Point ko floor par project karo, Pythagoras lagao (x2+y2), phir upar z jaake dobara Pythagoras lagao. Final: OP=x2+y2+z2. Bas yahi base hai — aage line, plane, vectors sab isi par bante hain.
