The angle between the line $\bar{r} = (\hat{i} + 2\hat{j} + \hat{k}) + \lambda(\hat{i} + \hat{j} + \hat{k})$ and the plane $\bar{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 8$ is $\ldots$

The acute angle between the lines $2x = 3y = -z$ and $6x = -y = -4z$ is $\ldots$

The maximum value of $z = 4x + y$ subject to the constraints $x + y \leq 5, 2x + y \leq 7, 3x + 2y \leq 11, x \geq 0, y \geq 0$ is $\ldots$

A fair die is thrown 4 times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is $\ldots$