For any two vectors `vec a` and `vec b`, we always have `|vec a+ vec b|<=|vec a|+|vec b|`

Explanation

To prove the inequality \( |\vec{a} + \vec{b}| \leq |\vec{a}| + |\vec{b}| \) for any two vectors \(\vec{a}\) and \(\vec{b}\), we can follow these steps:

### Step 1: Start with the expression for the magnitude of the sum of two vectors
We know that the magnitude of a vector can be expressed in terms of the dot product. Therefore, we can write:
\[ |\vec{a} + \vec{b}|^2 = (\vec{a} + \vec{b}) \cdot (\vec{a} + \vec{b}) \]

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