If `P` represents radiation pressure , `C` represents the speed of light , and `Q` represents radiation energy striking a unit area per second , then non - zero integers `x, y, z` such that `P^(x) Q^(y) C^(z)` is dimensionless , find the values of `x, y , and z`.

Explanation

To solve the problem, we need to find the non-zero integers \( x, y, z \) such that the expression \( P^x Q^y C^z \) is dimensionless. We will start by determining the dimensions of \( P \), \( Q \), and \( C \).

### Step 1: Determine the dimensions of \( P \) (radiation pressure)
Radiation pressure \( P \) has the same dimensions as pressure, which is defined as force per unit area.

- **Force** has dimensions of mass times acceleration:
\[
[F] = [M][A] = [M][L][T^{-2}]
...