Let the image of the point $P(1, 2, 6)$ in the plane passing through the points $A(1, 2, 0)$,$B(1, 4, 1)$,and $C(0, 5, 1)$ be $Q(\alpha, \beta, \gamma)$. Then $(\alpha^2 + \beta^2 + \gamma^2)$ is equal to :

If $(3,4,-7)$ is the foot of the perpendicular drawn from the point $(-2,3,6)$ to the plane $\pi$,then the sum of the intercepts made by the plane $\pi$ on the $X$ and $Y$-axes is

The length of the perpendicular drawn from the point $(2, 1, 4)$ to the plane containing the lines $\vec r = (\hat i + \hat j) + \lambda (\hat i + 2\hat j - \hat k)$ and $\vec r = (\hat i + \hat j) + \mu (-\hat i + \hat j - 2\hat k)$ is

If the image of the point $A(1, 1, 1)$ with respect to the plane $4x + 2y + 4z + 1 = 0$ is $B(\alpha, \beta, \gamma)$,then $\alpha + \beta + \gamma =$

Let $\bar{n}$ be a vector of magnitude $3\sqrt{3}$ such that it makes equal acute angles with the coordinate axes. Then the vector equation of a plane passing through $(1, -1, 2)$ and normal to $\bar{n}$ is:

The perpendicular distance from the origin to the plane containing the points having position vectors $\hat{i}+2\hat{j}+3\hat{k}$,$2\hat{i}+3\hat{j}-4\hat{k}$,and $3\hat{i}-4\hat{j}+5\hat{k}$ is