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

$A$ plane $\pi$ passing through the point $3 \hat{i}-4 \hat{j}+5 \hat{k}$ is parallel to the plane which passes through the point $\hat{i}+\hat{j}-\hat{k}$ and is perpendicular to the vector $\hat{i}+2 \hat{j}-3 \hat{k}$. Then the Cartesian equation of $\pi$ is

For what value of $k$ do the planes $kx + 4y + z = 0$,$4x + ky + 2z = 0$,and $2x + 2y + z = 0$ intersect in a single line?

The equation of a plane which passes through $(2, -3, 1)$ and is normal to the line joining the points $(3, 4, -1)$ and $(2, -1, 5)$ is given by

If a plane cuts the coordinate axes at $A, B$ and $C$ respectively such that the centroid of the triangle $ABC$ is $(6, 6, 3)$, then find the equation of that plane.

Find the distance from the origin to the plane passing through the point $(2, 3, -1)$ and perpendicular to the vector $3\hat{i} - 4\hat{j} + 7\hat{k}$.