Find the sum of the vectors ` veca= hat i-2 hat j+ hat k` , `vecb=-2 hat i+4 hat j+5 hat k` and `vecc= hat i-6 hat j-7 hat k`

Explanation

To find the sum of the vectors \(\vec{a} = \hat{i} - 2\hat{j} + \hat{k}\), \(\vec{b} = -2\hat{i} + 4\hat{j} + 5\hat{k}\), and \(\vec{c} = \hat{i} - 6\hat{j} - 7\hat{k}\), we will add them component-wise.

### Step 1: Write down the vectors
\[ \vec{a} = \hat{i} - 2\hat{j} + \hat{k} \]
\[
\vec{b} = -2\hat{i} + 4\hat{j} + 5\hat{k}
...