Show that the points `(a+5,a-4),(a-2,a+3) and (a,a)` do not lie on a straight line for any value of `a`.

Show that the points A(2, 3, -4), B(1, -2, 3) and C(3, 8, -11) are collinear.

Show that the point (3, -2, 4), (1, 1, 1) and (-1, 4,-2)are collinear.

Show that the points (2,3,-5) and (3,4,7) lie on the opposite side of the plane x+2y-2z=9

Show that points (0,1,2),(2,5,8),(5,6,6) and (3,2,0) from a parallelogram.

There are n+r points on a plane out of which n points lie on a straight line L and out of the remaining r points that lie outside L, no three points are collinear. What is the number of straight lines that can be formed by joining pairs of there points ?

Prove that the four points (0, 4, 3), (-1, -5, -3), (-2, -2, 1) and (1, 1, -1) lie in one plane. Find the equation of the plane.

Show that the line joining the points (0,2,-4) and (-1,1-2) and the lines joining the points (-2,3,3) and (-3,-2,1) are co-plannr. Find their point of intersection.

If the d.cs of a straight line be > , then what is the value of k ?