Find the dot product of $\mathbf{u}$ and $\mathbf{v}$.
\[
\mathbf{u}=3 \mathbf{i} \text { and } \mathbf{v}=-3 \mathbf{i}+5 \mathbf{j}
\]
$\mathbf{u} \cdot \mathbf{v}=$
(Simplify your answer.)
Answer
Final Answer: The dot product of \(\mathbf{u}\) and \(\mathbf{v}\) is \(\boxed{-9}\).
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 \(\boxed{-9}\).
