If vectors `hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk` are orthogonal to each other, then find the locus of th point (x,y).

Explanation

To solve the problem, we need to find the locus of the point \((x, y)\) such that the vectors \(\hat{i} - 2x\hat{j} - 3y\hat{k}\) and \(\hat{i} + 3x\hat{j} + 2y\hat{k}\) are orthogonal to each other.

### Step-by-Step Solution:

1. **Define the Vectors:**
Let
\[
\mathbf{A} = \hat{i} - 2x\hat{j} - 3y\hat{k}
...