Lines $\vec{r} = \vec{a} + \lambda\vec{b}$ and $\vec{r} = \vec{b} + \mu\vec{a}$ intersect at point $(2, 4, -4)$. If $|\vec{a} - \vec{b}| = 4$, then $\vec{a} \cdot \vec{b} =$

The Cartesian equations of the line passing through $A(0, 1, 1)$ and parallel to the X-axis are ....

The LPP maximize $z = 2x + 5y$ subject to $x + 3y \leq 6$, $2x + 6y \leq 18$, $x \geq 0$, $y \geq 0$ has

Four cards are drawn successively with replacement from well shuffled deck of 52 cards, then the probability that only two cards are club cards is ...........