Find the sum of the vectors ` -> a= hat i-2 hat j+ hat k , -> b=-2 hat i+4 hat j+5 hat k`and ` -> c= 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 follow these steps:

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

...