Let $\pi_1$ be the plane determined by the vectors $\hat{\mathbf{i}}+\hat{\mathbf{j}}$. $\hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\pi_2$ be the plane determined by the vectors $\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{k}}-\hat{\mathbf{i}}$. Let $\mathbf{a}$ be a non-zero vector parallel to the line of intersection of the planes $\pi_1$ and $\pi_2$. If $\mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$, then the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is

The variance of the discrete data $3,4,5,6,7,8,10,13$ is

If a number $x$ is drawn randomly from the set of numbers $\{1,2,3, \ldots ., 50\}$, then the probability that number $x$ that is drawn satisfies the inequation $x+\frac{10}{x} \leq 11$ is

If a coin is tossed seven times, then the probability of getting exactly three heads such that number two heads occur consecutively is