If $a, b, c$ are the intercepts made by the plane passing through the point $(1, 2, 3)$ parallel to the plane $3x + 4y - 5z = 0$ on the $X, Y, Z$-axes respectively,then $3a + b + 5c =$

Find the equation of the plane whose intercepts on the coordinate axes are $-4, 2$,and $3$.

The plane passing through $(2, 1, -3)$ and perpendicular to $3 \hat{i} - \hat{j} + 2 \hat{k}$ contains the points

$A$ plane at a unit distance from the origin intersects the three axes at points $P, Q,$ and $R$. If the centroid of $\Delta PQR$ is $(x, y, z)$,and it satisfies the equation $\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2} = k$,then find the value of $k$.

Let $\alpha x+\beta y+\gamma z=1$ be the equation of a plane passing through the point $(3, -2, 5)$ and perpendicular to the line joining the points $(1, 2, 3)$ and $(-2, 3, 5)$. Then the value of $\alpha \beta \gamma$ is equal to $..........$.

The mirror image of the point $P(-1, 2, -4)$ in the plane $x - y - 2z + 1 = 0$ is