If ` veca= hat i+ hat j+ hat k` ,` vec b=2 hat i- hat j+3 hat k` and ` vecc= hat i-2 hat j+ hat k` find a unit vector parallel to the vector `2 veca- vecb+3 vecc` .

Explanation

To find a unit vector parallel to the vector \( 2\vec{a} - \vec{b} + 3\vec{c} \), we will follow these steps:

### Step 1: Define the vectors
Given:
- \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \)
- \( \vec{b} = 2\hat{i} - \hat{j} + 3\hat{k} \)
- \( \vec{c} = \hat{i} - 2\hat{j} + \hat{k} \)

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