Given that the vector \( \mathbf{a} = x \mathbf{i} + 2 \mathbf{j} \) and the vector \( \mathbf{b} = 3 \mathbf{i} + y \mathbf{j} \) are orthogonal, find the values of variables \(x\) and \(y\).

Step 1 ：Step 1: We know that if two vectors are orthogonal, their dot product is zero. So we can write: \(\mathbf{a} . \mathbf{b} = 0\).

Step 2 ：Step 2: Substitute the given vectors into the equation: \(x*3 + 2*y = 0\).

Step 3 ：Step 3: Simplify the equation to get the values of \(x\) and \(y\): \(x = -2y/3\). However, this is not a specific solution because we don't have enough information to find the exact values of \(x\) and \(y\).