If a = (1, 1, 0) and b = (1, 1, 1), then unit vector in the plane of a and b and perpendicular to a is

The line passing through $$(1,1,-1)$$ and parallel to the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ meets the line $$\frac{x-3}{-1}=\frac{y+2}{5}=\frac{z-2}{-4}$$ at $$A$$ and the plane $$2 x-y+2 z+7=0$$ at $$B$$. Then $$A B$$ is equal to

Let $$\mathbf{a}=\hat{\mathbf{i}}$$ and $$\mathbf{b}=\hat{\mathbf{j}}$$, the point of intersection of the lines $$\mathbf{r} \times \mathbf{a}=\mathbf{b} \times \mathbf{a}$$ and $$\mathbf{r} \times \mathbf{b}=\mathbf{a} \times \mathbf{b}$$ is

The mean deviation from the mean of the set of observation $$-1,0,4$$ is