Step 1 :Given vectors are \(\mathbf{u}=3 \mathbf{i}\) and \(\mathbf{v}=-3 \mathbf{i}+5 \mathbf{j}\).
Step 2 :The dot product of two vectors is calculated by multiplying the corresponding components of the vectors and then adding those products together.
Step 3 :The i component of vector u is 3 and the i component of vector v is -3. The j component of vector u is not given, which means it is 0, and the j component of vector v is 5.
Step 4 :So, the dot product of u and v is \((3*-3) + (0*5) = -9\).
Step 5 :Final Answer: The dot product of \(\mathbf{u}\) and \(\mathbf{v}\) is \(\boxed{-9}\).