Verify that A(-1, 2, 1) B(1, -2, 5), C(4, -7, 8) and D(2, -3, 4) are the verticles of a parallelofram

Find the ratio in which the line segment joining the points (4, 4, -10) and (-2, 2, 4) is divided by the YZ-plane.

Prove that the triangle formed by joining the three points whose coordinates are A(1,2,3), B(2,3,1) and C(3,1,2), is an equilateral triangle.

Show that D(-1,4,-3) is the circumcentre of \(\Delta ABC\) with vertices A(3,2,-5), B(-3,8,-5) and C(-3,2,1).

A point is on the x-axis. What are its y-coordinate and z-coordinates?

Find the distance of point P(3,6,9) from the YZ-plane using distance formula.

Find the equation of the curve formed by the set of all points whose distances from the points (3,4,-5) and (-2,1,4) are equal.

Show that the points (0,7,10), (-1,6,6) and (-4,9,6) are the vertices of a right angled isosceles triangle.

Show that the points (-2,6,-2), (0,4,-1),(-2,3,1) and (-4,5,0) are the vertices of a squre.

Three points A(1,2,3), B(0,4,1) and C(-1,-1,-3) are the vertices of \(\Delta ABC\). Find the point in which the bisector of \(\angle BAC\) meets BC.

Two vertices of a triangle are A(3,4,2) and B(1,3,2). The medians of the triangle intersect at (2,4,3). Find the remaining vertex C of the triangle.

The mid-points of the sides of a triangle are (1,5,-1), (0,4,-2) and (2,3,4). Find its vertices

Three vertices of a parallelogram ABCD are A(3, – 1, 2), B (1, 2, – 4) and C (– 1, 1, 2). Find the coordinates of the fourth vertex.

Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0,4, 0) and (6, 0, 0).

If A and B be the points (3, 4, 5) and (–1, 3, –7), respectively, find the equation of the set of points P such that PA²+PB²=K² where k is a constant.