If $O(0,0,0), A(3,0,0), B(0,4,0)$ form a triangle,then the incentre of triangle $OAB$ is

If the origin is the centroid of the triangle for which $(-2, 3, 4)$ and $(3, -1, 5)$ are two vertices,then the third vertex is

In $\triangle ABC$,if the midpoints of the sides $AB, BC$ and $CA$ are respectively $(l, 0, 0), (0, m, 0)$ and $(0, 0, n)$,then $\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}=$

If $A \equiv (5, 1, p)$,$B \equiv (1, q, p)$,and $C \equiv (1, -2, 3)$ are the vertices of a triangle and $G \equiv (r, -\frac{4}{3}, \frac{1}{3})$ is its centroid,then the values of $p, q, r$ are respectively:

If the points $P = \hat{i} + 2 \hat{j}$,$Q = 4 \hat{i} + 6 \hat{j}$,$R = 5 \hat{i} + 7 \hat{j}$,and $S = a \hat{i} + b \hat{j}$ are the consecutive vertices of a parallelogram $PQRS$,then:

If the points $(-1, 3, 2)$,$(-4, 2, -2)$,and $(5, 5, \lambda)$ are collinear,then $\lambda = $