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

Consider a cuboid where all edges are integers and the base is a square. Suppose the sum of all its edges is numerically equal to the sum of the areas of all its six faces. Then,the sum of all its edges is

In $\triangle ABC$,the midpoints of the sides $AB, BC$ and $CA$ are respectively $(l, 0, 0), (0, m, 0)$ and $(0, 0, n)$. Then,$\frac{AB^2+BC^2+CA^2}{l^2+m^2+n^2}$ is equal to

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:

The four points $A(2,-1,3), B(4,-2,1), C(4,5,-7)$ and $D(2,6,-5)$ form a:

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