Let $\mathbf{s}=\langle-3,3\rangle$, and $\mathbf{t}=\langle 3,-4\rangle$. Perform the operations indicated. Write the vector answers in the form $\langle a, b\rangle$. \[ s+3 t \]

Step 1 ：Let vector \(\mathbf{s}=\langle-3,3\rangle\), and vector \(\mathbf{t}=\langle 3,-4\rangle\).

Step 2 ：We are asked to perform the operation \(s+3t\).

Step 3 ：First, we multiply vector \(\mathbf{t}\) by 3, which gives us \(\langle 9,-12 \rangle\).

Step 4 ：Then, we add this resulting vector to vector \(\mathbf{s}\). The addition of two vectors is done component-wise.

Step 5 ：So, the first component of the resulting vector is -3 + 9 = 6, and the second component is 3 + (-12) = -9.

Step 6 ：Thus, the result of the operation \(s + 3t\) is the vector \(\langle 6, -9 \rangle\).

Step 7 ：Final Answer: The result of the operation is the vector \(\boxed{\langle 6, -9 \rangle}\).