Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

Answer 1

$\mathbf u\cdot\mathbf v=\|\mathbf u\|\|\mathbf v\|\cos\theta$

where $\theta$ is the angle between the vectors. You have

$10\times9+6\times5=\sqrt{10^2+6^2}\sqrt{9^2+5^2}\cos\theta\iff \cos\theta=\dfrac{30}{\sqrt{901}}\implies \theta\approx1.909^\circ$

The vectors would be orthogonal if the dot product had been zero, but that's clearly not the case.

They would be parallel if the angle turned out to be $0^\circ$ or $180^\circ$, but that's also not the case.

So the answer is neither.