If $S$ is the set of all real values of $a$ such that a plane passing through the points $(-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2)$ also passes through the point $(-1, -1, 1)$,then $S=$

The intercepts of the plane $5x - 3y + 6z = 60$ on the coordinate axes are

The angle between the planes $2x - y + z = 6$ and $x + y + 2z = 3$ is

The equation of the plane,passing through the point $(-1, 2, -3)$ and parallel to the lines $\frac{x-1}{3} = \frac{y-2}{2} = \frac{z}{-4}$ and $\frac{x}{2} = \frac{y-1}{-3} = \frac{z-2}{2}$,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

Let $\pi_1$ be the plane passing through the points $(0,1,2), (1,0,-2), (-2,1,0)$ and $\pi_2$ be the plane passing through the point $(1,2,3)$ and perpendicular to the planes $x+y+z=1$ and $2x-3y+z=5$. If $\theta$ is the acute angle between the planes $\pi_1$ and $\pi_2$, then $\cos \theta=$