The vector equation of the line joining the points $i - 2j + k$ and $-2j + 3k$ is

The distance from the point $-i + 2j + 6k$ to the straight line passing through the point $(2, 3, -4)$ and parallel to the vector $6i + 3j - 4k$ is

If the harmonic conjugate of $P(2, 3, 4)$ with respect to the line segment joining the points $A(3, -2, 2)$ and $B(6, -17, -4)$ is $Q(\alpha, \beta, \gamma)$,then $\alpha + \beta + \gamma =$

If $A(3,-1,11)$,$B(0,2,3)$,and $C(4,8,11)$ are three points,then the coordinates of the foot of the perpendicular drawn from the point $A$ to the line joining the points $B$ and $C$ is

The orthocentre of the triangle formed by the points $(2,1,5)$,$(3,2,3)$,and $(4,0,4)$ is

Let a line $L$ passing through the point $(1, 1, 1)$ be perpendicular to both the vectors $2\hat{i} + 2\hat{j} + \hat{k}$ and $\hat{i} + 2\hat{j} + 2\hat{k}$. If $P(a, b, c)$ is the foot of the perpendicular from the origin on the line $L$,then the value of $34(a + b + c)$ is: