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 co-ordinates of the point where the line joining the points $(3,5,-7)$ and $(-2, 1, 8)$ is intersected by the YOZ plane are

If the lines $\vec{r} = (\hat{i} + m\hat{j} + 3\hat{k}) + \lambda(2\hat{i} + 3\hat{j} + 4\hat{k})$ and $\vec{r} = (4\hat{i} + \hat{j}) + \mu(5\hat{i} + m\hat{j} + \hat{k})$ intersect each other, then m =