The equation of the plane passing through the points $(1, 2, 3)$,$(-1, 4, 2)$ and $(3, 1, 1)$ is

The Cartesian equation of the plane passing through the point $(3, -2, -1)$ and parallel to the vectors $\vec{b} = \hat{i} - 2\hat{j} + 4\hat{k}$ and $\vec{c} = 3\hat{i} + 2\hat{j} - 5\hat{k}$ is:

Find the equation of the plane passing through the points $(2, 1, 0)$,$(3, -2, -2)$,and $(3, 1, 7)$.

If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are three non-coplanar vectors, then the vector equation $\overrightarrow{r}=(1-p-q) \overrightarrow{a}+p \overrightarrow{b}+q \overrightarrow{c}$ represents a :

Find the equation of the planes bisecting the angles between the planes $\vec{r} \cdot (\hat{i} + 2\hat{j} + 2\hat{k}) = 19$ and $\vec{r} \cdot (4\hat{i} - 3\hat{j} + 12\hat{k}) + 3 = 0$.

The equation of the plane passing through the midpoint of the line segment joining the points $A(4, 5, -10)$ and $B(-1, 2, 1)$ and perpendicular to $AB$ is: