Step-by-step Solution:

\[Statement A:\] Two vectors are said to be identical if their difference is zero. Mathematically, if \( \mathbf{A} - \mathbf{B} = 0 \), then \( \mathbf{A} = \mathbf{B} \), which means the vectors are identical. This statement is true. \[Statement B:\] Velocity is not a vector quantity. Velocity is defined as a vector quantity because it has both magnitude and direction. This statement contradicts the fundamental definition of velocity. This statement is false. \[Statement C:\] Projection of one vector on another is not an application of dot product. The projection of a vector \( \mathbf{A} \) on another vector \( \mathbf{B} \) is given by: \[ \text{Proj}_{\mathbf{B}} \mathbf{A} = \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{B}|^2} \mathbf{B} \] Since dot product \( \mathbf{A} \cdot \mathbf{B} \) is used in the formula, vector projection is an application of dot product. This statement is false. \[Statement D: \] The maximum space rate of change of a function in the increasing direction of the function is known as the gradient of a scalar function. The gradient of a scalar function \( f(x, y, z) \) is given by: \[ \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right) \] The gradient represents the direction of the maximum rate of increase of the function. This statement is true. Correct Answer: From the analysis above: - A and D are correct. - B and C are incorrect. Thus, the correct option is: \[ \boxed{\text{C. A and D only}} \]