Young Physicist — CP

Understanding the problem

We’re given n force vectors in 3D space, each with x, y, z components. We need to check if the body is in equilibrium — meaning the sum of all forces equals zero.

A body is in equilibrium when the resultant force is (0, 0, 0). So we just need to check if the sum of all x components = 0, sum of all y = 0, and sum of all z = 0.

My thinking

This was my first instinct and it turned out to be exactly right:

Sum all x values → should be 0
Sum all y values → should be 0
Sum all z values → should be 0

If all three sums are 0 → print YES, else NO.

No tricks, no edge cases. Just careful reading.

Code

#include <bits/stdc++.h>
using namespace std;

int main(){
    int n;
    int vectorA = 0;
    int vectorB = 0;
    int vectorC = 0;

    cin >> n;

    for(int i = 0; i < n; i++){
        for(int j = 0; j < 3; j++){
            int vector;
            cin >> vector;
            if(j == 0) vectorA += vector;
            else if(j == 1) vectorB += vector;
            else vectorC += vector;
        }
    }

    if(vectorA == 0 && vectorB == 0 && vectorC == 0){
        cout << "YES" << endl;
        return 0;
    }

    cout << "NO" << endl;
}

What I learned

Reading 3D vectors row by row using a nested loop with j tracking the component index
break only exits the innermost loop — caught this when debugging the next problem
For equilibrium problems, always think resultant vector = zero vector