If A (6,-6,0), B(-1,-7,6), C (3,-4, 4) and D (2,-9,2) be four points in space. Show that AB is perpendicular to CD.

A(0,5,6),B(1,4,7),C(2,3,7) and D(3,4,6) are four points in space. The point nearest to the origin O(0,0,0) is (A) A (B) B (C) C (D) D

If points A (2, 4, 0), B(3, 1, 8), C(3, 1, -3), D(7, -3, 4) are four points then projection of line segment AB on line CD.

Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6) and D(2,-5,10) are such that AB and CD intersect at the point P(1,-1,2) .

Using vectors show that the points A(-2,3,5), B(7,0,-1), C(-3,-2,-5) and D(3,4,7) are such that AB and CD intersect at the point P(1,2,3).

Show that the point A(4,-1,2), B(-3,5,1), C(2,3,4) and D(1,6,6) are coplanar. Also find the equation of the plane passing through these points.

Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d D(2,-5,10) are such that A B and C D intersect at the point P(1,-1,2)dot

Show that the points A (5, 6), B(1,5), C(2, 1) and D(6, 2) are the vertices of a square ABCD.

Prove that the points A (9,0) , B(9,6) , C (-9 , 6) and D (-9,0) are the vertices of a rectangle .

Points A (-3, -2), B (-6, a), C (-3, -4) and D(0, -1) are thte vertices of quadrilateral ABCD, find a if 'a' is negative and AB = CD

Four points A(6,\ 3),\ \ B(-3,\ 5),\ \ C(4,\ -2) and D(x ,\ 2x) are given in such a way that area of ( D B C)/( A B C)=1/2 , find x .