Find the dot product of $\begin{pmatrix} 3 \\ -4 \\ -3 \end{pmatrix}$ and $\begin{pmatrix} -5 \\ 2 \\ 1 \end{pmatrix}.$
To find the dot product of two vectors, I need to multiply the corresponding components and add them up. So, the dot product is $(3)(-5) + (-4)(2) + (-3)(1)$. This simplifies to $-15 - 8 - 3$, which is $-26$. 