Answer
The pair of vectors is not orthogonal.
Work Step by Step
Step 1: According to vector notation, $\textbf {u}=\langle -4,3 \rangle$ and $\textbf {v}=\langle 8,-6 \rangle$
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: $\cos\theta=\frac{\langle -4,3 \rangle\cdot\langle 8,-6 \rangle}{|\langle -4,3 \rangle||\langle 8,-6 \rangle|}$
Step 4: $\cos\theta=\frac{-4(8)+3(-6)}{\sqrt ((-4)^{2}+(3)^{2})\cdot\sqrt ((8)^{2}+(-6)^{2})}$
Step 5: $\cos\theta=\frac{-32-18}{\sqrt (16+9)\cdot\sqrt (64+36)}$
Step 6: $\cos\theta=\frac{-50}{\sqrt (25)\cdot\sqrt (100)}$
Step 7: $\cos\theta=\frac{-50}{5\times10}$
Step 8: $\cos\theta=\frac{-50}{50}$
Step 9: $\cos\theta=-1$
Step 10: $\theta=\cos^{-1}(-1)$
Step 11: Solving using the inverse cos function on the calculator,
$\theta=\cos^{-1}(-1)=180^{\circ}$
Since the angle between the two vectors is not $90^{\circ}$, the two vectors are not orthogonal.
