The co-ordinates of the points P,Q,R and S are (1, 1, 1),(-2,4, 1),(- 1, 5, 5) and (2, 2, 5). Prove that PQRS is a square.

The coordinates of the points A , B , C and D are ( 1 , 1 , 1) , ( -2 , 4 , 1) , ( - 1 , 5 , 5) and ( 2 , 2 , 5) , prove that ABCD is a square .

Prove that the four ponts (1,1,1),(-2,4,1),(-1,5,5) and (2,2,5) are the vertices of a square.

Show that the points (1,1,1), (-2,4,1), (-1,5,5) & (2,2,5) form a square.

The distance between the points A(5,1,2) and B(4,6,-1)is

Find the co-ordinates of the point of trisection of the line segment joining the points (0, 2, 1) and (2, -1, 5) that is nearer to (0, 2, 1).

Using direction numbers show that points P(4, 7, 8) and Q(2, 3, 4), R(-1, -2, 1) and S(1, 2, 5) taken in order, are the vertices of a parallelogram. Is the parallelogram a rectangle?

The co-ordinates of end points of a focal chord of an ellipse are (x_1,y_1) and (x_2,y_2) .Prove that y_1y_2+4x_1x_2=0

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

Calculating the angle of the triangle, prove that the points A(3, 4, -1) , B(1, 5, 1) and C(1, 2, -2) are the vertices of an isosceles triangle.

The distance between the points A (5 , 1 , 2 ) and B (4 , 6 , -1) is