Answer
The pair of vectors is not orthogonal.
Work Step by Step
Step 1: We let $\textbf {u}=\langle 3,4 \rangle$ and $\textbf {v}=\langle 6,8 \rangle$
Step 2: We substitute vectors $\textbf {u}$ and $\textbf {v}$ in the formula for finding the angle between a pair of vectors, $\cos\theta=\frac{\textbf {u}\cdot\textbf {v}}{|\textbf {u}||\textbf {v}|}$
Step 3: $\cos\theta=\frac{\langle 3,4 \rangle\cdot\langle 6,8 \rangle}{|\langle 3,4 \rangle||\langle 6,8 \rangle|}$
Step 4: $\cos\theta=\frac{3(6)+4(8)}{\sqrt (3^{2}+4^{2})\cdot\sqrt (6^{2}+8^{2})}$
Step 5: $\cos\theta=\frac{18+32}{\sqrt (9+16)\cdot\sqrt (36+64)}$
Step 6: $\cos\theta=\frac{50}{\sqrt (25)\cdot\sqrt (100)}$
Step 7: $\cos\theta=\frac{50}{5\times10}=1$
Step 8: $\theta=\cos^{-1}(1)$
Step 9: Solving using the inverse cos function on the calculator,
$\theta=\cos^{-1}(1)=0^{\circ}$
Since the angle between the two vectors is not $90^{\circ}$, the two vectors are not orthogonal.