Prove that the points `(p,p^(2)),(q,q^(2))and(r,r^(2))(pner)` can never be collinear.

Prove that the points (p,p^(2)), (q,q^(2))and(r,r^(2))(pneqner) can never be collinear.

If a ,b ,c are the p t h ,q t h ,r t h terms, respectively, of an HP , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.

Prove that the points P(-1,-2) Q (7,4) R (4,8) and S(-4,2) are the vertices of a rectangle.

Using direction ratios show that the points P(2, 3, 4) Q(-1, -2, 1) and R(5, 8, 7) are collinear.

Show that the points (p , q , r) , (q , r , p) and (r , p , q) are the vertices of an equilateral triangle.

Show that the points P(-2,3,5) ,Q (1,2,3) and R (7,0,-1) are collinear

If the points P (0,3,2), Q(1,2,-2) and R (4,-1,t) are collinear, find the value of t.

If the points P (1,2,3), Q(4,5,6) and R(7,8,9) are collinear then Q divides PR in the ratios of -

The vertices of a triangle are (p q ,1/(p q)),(q r ,1/(q r)), and (r p ,1/(r p)), where p ,q and r are the roots of the equation y^3-3y^2+6y+1=0 . The coordinates of its centroid are

The ratio in which he line-segment joining the points (p,q,r) and (-p, -r, -q) is divided by the zx-plane, is-