To solve this problem, we need to determine which of the given vectors is orthogonal to $\mathbf{v} = 7\mathbf{i} - 4\mathbf{j}$. Two vectors are orthogonal if their dot product equals zero.

The dot product of two vectors $\mathbf{a} = a_1\mathbf{i} + a_2\mathbf{j}$ and $\mathbf{b} = b_1\mathbf{i} + b_2\mathbf{j}$ is calculated as: $\mathbf{a} \cdot \mathbf{b} = a_1b_1 + a_2b_2$

For $\mathbf{v} = 7\mathbf{i} - 4\mathbf{j}$, we test the dot product with each given vector