Find the Cartesian equation of the plane passing through the point with position vector $2\hat{i} + 3\hat{j} - 4\hat{k}$ and perpendicular to the vector $2\hat{i} - \hat{j} + 2\hat{k}$.

Let $P$ be a plane passing through the points $(2,1,0)$,$(4,1,1)$,and $(5,0,1)$,and $R$ be the point $(2,1,6)$. Then the image of $R$ in the plane $P$ is:

If $L_1$ and $L_2$ are two lines which pass through the origin and have direction ratios $(3, 1, -5)$ and $(2, 3, -1)$ respectively,then the equation of the plane containing $L_1$ and $L_2$ is

The $x$-intercept of a plane $\pi$ passing through the point $(1,1,1)$ is $\frac{5}{2}$ and the perpendicular distance from the origin to the plane $\pi$ is $\frac{5}{7}$. If the $y$-intercept of the plane $\pi$ is negative and the $z$-intercept is positive,then its $y$-intercept is

If for a plane,the intercepts on the coordinate axes are $8, 4, 4$,then the length of the perpendicular from the origin onto the plane is:

The volume (in cubic units) of the tetrahedron bounded by the plane $3x + 4y - 5z = 60$ and the three coordinate planes is