$A$ plane which bisects the angle between the two given planes $2x - y + 2z - 4 = 0$ and $x + 2y + 2z - 2 = 0$,passes through the point

If the plane $7x + 11y + 13z = 3003$ meets the coordinate axes at $A, B, C$,then the centroid of the $\triangle ABC$ is

If $\alpha$ is the acute angle between the planes $P_1$ and $P_2$,where the combined equation of the planes $P_1$ and $P_2$ is $2x^2 - 6y^2 - 12z^2 + 18yz + 2zx + xy = 0$,then the value of $\cos \alpha$ is:

If the planes $\bar{r} \cdot(2 \hat{i}-\lambda \hat{j}+\hat{k})=3$ and $\bar{r} \cdot(4 \hat{i}-\hat{j}+\mu \hat{k})=5$ are parallel,then the values of $\lambda$ and $\mu$ are respectively:

The equation of the plane containing the lines $r = a_1 + \lambda a_2$ and $r = a_2 + \lambda a_1$ is

If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^{2}(z-12)^{2}} + \frac{y-19}{(x-11)^{2}(z-12)^{2}} + \frac{z-12}{(x-11)^{2}(y-19)^{2}} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is: