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 =

If the lines $x = -1 + s$, $y = 3 - \lambda s$, $z = 1 + \lambda s$ and $x = \dfrac{t}{2}$, $y = 1 + t$, $z = 2 - t$ with parameters s and t, are coplanar, then $\lambda =$

The equation of the plane passing through the point $(1,2,1)$ and perpendicular to the planes $x + 2y + 2z - 7 = 0$ and $3x + 3y + 2z - 5 = 0$ is