The equation of a plane which cuts equal intercepts of unit length on the axes is:

Find the equation of the plane passing through $(a, b, c)$ and parallel to the plane $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=2$.

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

If the distance between the planes $4x - 2y - 4z + 1 = 0$ and $4x - 2y - 4z + d = 0$ is $7$,then the value of $d$ is:

The equation of the plane which is parallel to the plane $x - 2y + 2z = 5$ and whose distance from the point $(1, 2, 3)$ is $1$ is:

In the following cases,determine whether the given planes are parallel or perpendicular,and in case they are neither,find the angle between them:
$4x + 8y + z - 8 = 0$ and $y + z - 4 = 0$