The sum of the three vectors shown in figure is zero. Find the magnitudes of the vectors `vec(OB) and vec(OC)`.

Explanation

To solve the problem of finding the magnitudes of the vectors \(\vec{OB}\) and \(\vec{OC}\) given that the sum of three vectors \(\vec{OA}\), \(\vec{OB}\), and \(\vec{OC}\) is zero, we can follow these steps:

### Step 1: Define the vectors
- The vector \(\vec{OA}\) has a magnitude of 5 units and is directed downwards along the negative y-axis. Therefore, we can express it as:
\[ \vec{OA} = -5 \hat{j} \]

...