If the plane $3x - 2y - z - 18 = 0$ meets the coordinate axes at $A, B, C$,then the centroid of $\triangle ABC$ is

Find the equation of the set of points which are equidistant from the points $(1, 2, 3)$ and $(3, 2, -1)$.

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

The equation of the $yz$-plane is

Let $\pi_1$ be the plane determined by the vectors $\hat{i}+2 \hat{j}$ and $3 \hat{j}-2 \hat{k}$. Let $\pi_2$ be the plane determined by the vectors $\hat{j}+2 \hat{k}$ and $3 \hat{k}-2 \hat{i}$. If $\theta$ is the angle between $\pi_1$ and $\pi_2$,then $\cos \theta=$

The equation of the plane passing through the point $(2, -1, -3)$ and parallel to the lines $\frac{x-1}{3} = \frac{y+2}{2} = \frac{z}{-4}$ and $\frac{x}{2} = \frac{y-1}{-3} = \frac{z-2}{2}$ is: