Answer
The pair of vectors is orthogonal.
Work Step by Step
Step 1: We let $\textbf {u}=\langle 1,1 \rangle$ and $\textbf {v}=\langle 1,-1 \rangle$
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: $\cos\theta=\frac{\langle 1,1 \rangle\cdot\langle 1,-1 \rangle}{|\langle 1,1 \rangle||\langle 1,-1 \rangle|}$
Step 4: $\cos\theta=\frac{1(1)+1(-1)}{\sqrt (1^{2}+1^{2})\cdot\sqrt ((-1)^{2}+1^{2})}$
Step 5: $\cos\theta=\frac{1-1}{\sqrt (1+1)\cdot\sqrt (1+1)}$
Step 6: $\cos\theta=\frac{0}{\sqrt (2)\cdot\sqrt (2)}$
Step 7: $\cos\theta=0$
Step 8: $\theta=\cos^{-1}(0)$
Step 9: Solving using the inverse cos function on the calculator,
$\theta=\cos^{-1}(0)=90^{\circ}$
Since the angle between the two vectors is $90^{\circ}$, the two vectors are perpendicular and thus orthogonal.
