Answer
The pair of vectors is not orthogonal.
Work Step by Step
Step 1: We let $\textbf {u}=\langle 1,0 \rangle$ and $\textbf {v}=\langle \sqrt 2,0 \rangle$
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: $\cos\theta=\frac{\langle 1,0 \rangle\cdot\langle \sqrt 2,0 \rangle}{|\langle 1,0 \rangle||\langle \sqrt 2,0 \rangle|}$
Step 4: $\cos\theta=\frac{1(\sqrt 2)+0(0)}{\sqrt (1^{2}+0^{2})\cdot\sqrt ((\sqrt 2)^{2}+0^{2})}$
Step 5: $\cos\theta=\frac{\sqrt 2+0}{\sqrt (1+0)\cdot\sqrt (2+0)}$
Step 6: $\cos\theta=\frac{\sqrt 2}{\sqrt 1\cdot\sqrt 2}$
Step 7: $\cos\theta=\frac{1}{\sqrt 1}=1$
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.
