If the planes $x + 2y + kz = 0$ and $2x + y - 2z = 0$ are at right angles,then the value of $k$ is

$A$ plane meets the coordinate axes at $P, Q,$ and $R$ such that the position vector of the centroid of $\Delta PQR$ is $2i - 5j + 8k$. Then the equation of the plane is:

$A$ 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

If $O$ is the origin and $A$ is the point $(a, b, c)$,then the equation of the plane passing through $A$ and perpendicular to $OA$ is:

$P$ and $Q$ are points on the straight line passing through the point $A(3 \hat{i}+\hat{j}-\hat{k})$ and parallel to the vector $\vec{v} = 2 \hat{i}-\hat{j}+2 \hat{k}$. If $AP = AQ = 3$,then the vector equation of the plane $OPQ$ is:

If $A(-1, 2, 3)$,$B(1, 1, 1)$ and $C(2, -1, 3)$ are points on a plane,then a unit normal vector to the plane $ABC$ is: