If the product of the distances of the point (1, 2, 3) from the origin and the plane $2x - 3y + z + k = 0$ is 7, then the value of k is

The vector equation of the line whose cartesian equations are $x = 2, 2y - 3z + 7 = 0$

The feasible region represented by the constraints $y - 2x \leq 4, x + y \geq 5, x \leq 4, y \geq 2, x, y \geq 0$ is ...........

A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that the number obtained on the die is an odd number.
Let $p : P(A) = \dfrac{1}{3}$, $q$ : A and B are independent events.
Then the truth values of statements $p$ and $q$ respectively are.....