$A$ line joining the points $(1, 2, 0)$ and $(4, 13, 5)$ is perpendicular to a plane. Then the coefficients of $x, y$ and $z$ in the equation of the plane are respectively

If the plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{3} = 1$ intersects the coordinate axes at $A, B, C$,then the area of $\Delta ABC$ is:

If the plane $-4x - 2y + 2z + \alpha = 0$ is at a distance of $2$ units from the plane $2x + y - z + 1 = 0$, then the product of all the possible values of $\alpha$ is

If the cartesian equation of the plane passing through the point $\hat{i}+2 \hat{j}+\hat{k}$ and parallel to the vectors $2 \hat{i}+3 \hat{j}+\hat{k}$ and $-\hat{i}+2 \hat{j}-3 \hat{k}$ is $a x+b y+c z=1$, then $18(a+b+c)$ is equal to

If planes $\vec{r} \cdot (p \hat{i} - \hat{j} + 2 \hat{k}) + 3 = 0$ and $\vec{r} \cdot (2 \hat{i} - p \hat{j} - \hat{k}) - 5 = 0$ include an angle $\frac{\pi}{3}$,then the value of $p$ is

The distance of the plane $\vec{r} = (\hat{i} - \hat{j}) + \lambda(\hat{i} + \hat{j} + \hat{k}) + \mu(\hat{i} - 2\hat{j} + 3\hat{k})$ from the origin is