### Instruction: Find $x$ so that the vectors $\begin{pmatrix} 2 \\ 5 \end{pmatrix}$ and $\begin{pmatrix} x \\ -3 \end{pmatrix}$ are orthogonal.### Response: What does it mean for two vectors to be orthogonal?
It means that their dot product is 0.
Ok, so we need to find $x$ so that $2*x + 5*-3 = 0$.
That means $2x-15=0$.