Find the sum of vectors ` vec a= hat i-2 hat j+ hat k ,\ vec b=-2 hat i+4 hat j+5 hat k\ a n d\ vec c= hat i-6 hat j-7 hat kdot`

Explanation

To find the sum of the vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\), we will follow these steps:

### Step 1: Write down the vectors
We have the following vectors:
- \(\vec{a} = \hat{i} - 2\hat{j} + \hat{k}\)
- \(\vec{b} = -2\hat{i} + 4\hat{j} + 5\hat{k}\)
- \(\vec{c} = \hat{i} - 6\hat{j} - 7\hat{k}\)

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