When a vector `vecC` is added to the resultant of vectors
`vecA=hati+4hatj-2hatk and vecB=3hati-5hatj+hatk`, a unit vector along
Z-axis is obtained . Find the vector `vecC`

Explanation

To find the vector \( \vec{C} \) that, when added to the resultant of vectors \( \vec{A} \) and \( \vec{B} \), gives a unit vector along the Z-axis, we can follow these steps:

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