If $a, b, c$ are distinct non-negative numbers and the vectors $a\hat{i} + a\hat{j} + c\hat{k}, \hat{i} + \hat{k}, c\hat{i} + c\hat{j} + b\hat{k}$ lie in the same plane, then the value of $c$ is...

Let $A(2,3,0)$, $B(0,3,2)$ and $C(4,0,3)$ be vertices of a triangle, then the area of the triangle is

If D and E are the midpoints of the sides BA and BC of triangle ABC, then $\overline{AE} + \overline{DC} = $

If the points $(1, 1, \mu)$ and $(-3, 0, 1)$ are equidistant from the plane $\vec{r} \cdot (3\hat{i} + 4\hat{j} - 12\hat{k}) + 13 = 0$, then the value of $\mu$ are