Find the equation of the plane with intercepts $2, 3$ and $4$ on the $x, y$ and $z$-axis respectively.

The locus of a first degree equation in $x, y, z$ is a

If the angle between the planes $ax - y + 3z = 2a$ and $3x + ay + z = 3a$ is $\frac{\pi}{3}$, then the direction ratios of the line perpendicular to the plane $(a+2)x + (a-4)y + 2az = a$ are

If the cartesian equation of the plane passing through the point $\hat{i}+2 \hat{j}+\hat{k}$ and parallel to the vectors $2 \hat{i}+3 \hat{j}+\hat{k}$ and $-\hat{i}+2 \hat{j}-3 \hat{k}$ is $a x+b y+c z=1$, then $18(a+b+c)$ is equal to

Find the Cartesian equation of the following plane: $\vec{r} \cdot (2\hat{i} + 3\hat{j} - 4\hat{k}) = 1$

The equation of the plane whose intercepts on $x, y, z$ axes are $1, 2, 4$ respectively is