The dot product of two vectors $\mathbf{u}=\langle u_1,u_2\rangle$ and $\mathbf{v}=\langle v_1,v_2\rangle$ is given by $u_1v_1 + u_2v_2$. So, for $\mathbf{u}=\langle 1,1\rangle$ and $\mathbf{v}=\langle 2,-2\rangle$, the dot product is $1*2 + 1*(-2) = 0$.
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