6. When rolling a die twice, the numbers obtained are $m, n$, and the vector $a=(m, n)$ is formed. Then the probability that the angle between $a$ and $b=(1,-1)$ is an angle in a right triangle is $\qquad$
6. $\frac{7}{12}$.

Since $m, n$ can both take values from $1 \sim 6$, the vector $a$ has