If `veca=hati+hatj+hatk,hatb=hati-hatj+hatk,vecc=hati+2hatj-hatk`, then find the value of `|{:(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.vecc):}|`

Explanation

To solve the problem, we need to calculate the dot products of the given vectors and then find the determinant of the resulting matrix. Let's go through the steps systematically.

### Given Vectors:
1. \(\vec{a} = \hat{i} + \hat{j} + \hat{k}\)
2. \(\vec{b} = \hat{i} - \hat{j} + \hat{k}\)
3. \(\vec{c} = \hat{i} + 2\hat{j} - \hat{k}\)

### Step 1: Calculate the dot products
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