$A$ plane passing through $(-1, 2, 3)$ and whose normal makes equal angles with the coordinate axes is

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 $\cos \theta=$

Two systems of rectangular axes have the same origin. If a plane cuts them at distances $a, b, c$ and $a', b', c'$ from the origin along the axes,then:

$A$ plane passing through the point $(3,1,1)$ contains two lines whose direction ratios are $1, -2, 2$ and $2, 3, -1$ respectively. If this plane also passes through the point $(\alpha, -3, 5)$,then $\alpha$ is equal to

The vector equation of the plane passing through the point $2\hat{i} - \hat{j} - 4\hat{k}$ and parallel to the plane $\vec{r} \cdot (4\hat{i} - 12\hat{j} - 3\hat{k}) - 7 = 0$ is:

The distance between the two planes $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is