If the points $A(0, 1, 2)$,$B(2, -1, 3)$,and $C(1, -3, 1)$ are the vertices of a triangle,then the triangle is

Let $ABCD$ be a parallelogram and $E$ be the mid-point of $AB$. If $P$ is the point of intersection of $DE$ and $AC$,then $\frac{DP}{PE} + \frac{AP}{PC} = $

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

Verify that the points $(0, 7, -10)$,$(1, 6, -6)$,and $(4, 9, -6)$ are the vertices of an isosceles triangle.

If $A(1,4,2)$ and $C(5,-7,1)$ are two vertices of triangle $ABC$ and $G\left(\frac{4}{3}, 0, \frac{-2}{3}\right)$ is the centroid of the triangle $ABC$,then the midpoint of side $BC$ is

If the circumcenter of the triangle formed by the points $(1,2,3), (3,-1,5)$ and $(4,0,-3)$ is $(\alpha, \beta, \gamma)$, then $|\alpha|+|\beta|=$