The formula `(veca+vecb)^(2)=vec(a^(2))+vec(b^(2))+2vecaxxvecb` is valid for non-zero vectors `vecaandvecb`.

Explanation

To determine if the formula \((\vec{a} + \vec{b})^2 = \vec{a}^2 + \vec{b}^2 + 2\vec{a} \times \vec{b}\) is valid for non-zero vectors \(\vec{a}\) and \(\vec{b}\), we will analyze the left-hand side and the right-hand side of the equation.

### Step 1: Expand the left-hand side
The left-hand side of the equation is \((\vec{a} + \vec{b})^2\). By the definition of the square of a vector sum, we can expand this as follows:

\[ (\vec{a} + \vec{b})^2 = (\vec{a} + \vec{b}) \cdot (\vec{a} + \vec{b}) \]
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