Find a vector of magnitude 5 units, and parallel to the resultant of the vectors ` vec a=2 hat i+3 hat j- hat k` and ` vec b= hat i-2 hat j+ hat k`.

Explanation

To solve the problem, we need to find a vector of magnitude 5 units that is parallel to the resultant of the vectors \(\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}\) and \(\vec{b} = \hat{i} - 2\hat{j} + \hat{k}\).

### Step-by-Step Solution:

**Step 1: Find the resultant vector \(\vec{c}\) of \(\vec{a}\) and \(\vec{b}\).**

The resultant vector \(\vec{c}\) can be found by adding the corresponding components of \(\vec{a}\) and \(\vec{b}\):

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