Answer
Orthogonal vectors
Work Step by Step
If $ u \cdot v = 0 $ for two nonzero vectors $u=\left\langle a,b\right\rangle$, $v=\left\langle c,d\right\rangle$, then $\cos \theta = 0 $ means $\theta= 90°$ and the vectors $u$ and $v$ are called orthogonal vectors.
The dot product is given by:
$u\cdot v=\left\langle a,b\right\rangle\cdot\left\langle c,d\right\rangle=ac+bd$
Now for $\left\langle 1,1\right\rangle$ and $\left\langle 1,-1\right\rangle$ we have
$\left\langle 1,1\right\rangle\cdot\left\langle 1,-1\right\rangle=(1)(1)+(1)(-1)=1-1=0$.
Since $\left\langle 1,1\right\rangle\cdot\left\langle 1,-1\right\rangle=0$ therefore, the vectors $\left\langle 1,1\right\rangle$ and $\left\langle 1,-1\right\rangle$ are orthogonal vectors (to each other).
