Find the vector that must be added to the vector `hat(i)-3hat(j)+2hat(k)` and `3hat(i)+6hat(j)-7hat(k)` so that the resultant vector is a unit vector along the y-axis.

Explanation

To solve the problem, we need to find the vector that must be added to the given vectors such that the resultant vector is a unit vector along the y-axis. Let's break down the steps:

### Step 1: Identify the Given Vectors
The two vectors provided are:
1. \( \vec{A} = \hat{i} - 3\hat{j} + 2\hat{k} \)
2. \( \vec{B} = 3\hat{i} + 6\hat{j} - 7\hat{k} \)

### Step 2: Find the Resultant Vector
...