vectors `veca,vecb and vecc` are of the same length and when taken pair-wise they form equal angles. If `veca=hati+hatj and vecb=hatj+hatk` then find vector `vecc`.

Explanation

To find the vector \(\vec{c}\) given that vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are of the same length and form equal angles with each other, we can follow these steps:

### Step 1: Define the vectors
We have:
\[ \vec{a} = \hat{i} + \hat{j} \]
\[
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