The locus represented by $xy + yz = 0$ is

$A$ variable plane is at a constant distance $p$ from the origin and meets the axes in $A, B$ and $C$. The locus of the centroid of the tetrahedron $OABC$ is

$A$ plane is parallel to two lines whose direction ratios are $2, 0, -2$ and $-2, 2, 0$ and it contains the point $(2, 2, 2)$. If it cuts the coordinate axes at $A, B, C$,then the volume of the tetrahedron $OABC$ (in cubic units) is

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

$A$ plane $P$ is parallel to two lines whose direction ratios are $-2, 1, -3$ and $-1, 2, -2$,and it contains the point $(2, 2, -2)$. Let $P$ intersect the coordinate axes at the points $A, B, C$ making the intercepts $\alpha, \beta, \gamma$. If $V$ is the volume of the tetrahedron $OABC$,where $O$ is the origin and $p = \alpha + \beta + \gamma$,then the ordered pair $(V, p)$ is equal to.

In the following cases,determine whether the given planes are parallel or perpendicular,and in case they are neither,find the angle between them: $7x + 5y + 6z + 30 = 0$ and $3x - y - 10z + 4 = 0$.