NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter : INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

Short Answer Type

In which octant do the points lie?

Find the coordinates of the feet of perpendiculars from a point P on the xy, yz and zx-planes respectively for the given cases.

Find how far apart the points (2, 0, 0) and (−3, 0, 0) are.

Find the distance from the origin to the point (6, 6, 7).

Show that if \(x^2 + y^2 = 1\), then the point \((x, y, \sqrt{1 - x^2 - y^2})\) is at a distance 1 unit from the origin.

Show that the points A (1, −1, 3), B (2, −4, 5) and (5, −13, 11) are collinear.

Three consecutive vertices of a parallelogram ABCD are A (6, −2, 4), B (2, −4, −8), and C (−2, 2, 4). Find the coordinates of the fourth vertex.

Show that the triangle ABC with vertices A (0, 4, 1), B (2, 3, −1) and C (4, 5, 0) is right angled.

Find the third vertex of a triangle whose centroid is origin and two vertices are (2, 4, 6) and (0, −2, −5).

Find the centroid of a triangle the mid-point of whose sides are given as D (1, 2, −3), E (3, 0, 1), and F (−1, 1, −4).

The mid-points of the sides of a triangle are (5, 7, 11), (0, 8, 5), and (2, 3, −1). Find its vertices.

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

Find the coordinates of the points which trisect the line segment joining A (2, 1, −3) and B (5, −8, 3).

If the origin is the centroid of a triangle ABC having vertices A (a, 1, 3), B (−2, b, −5), and C (4, 7, c), find the values of a, b, c.

Let A (2, 2, −3), B (5, 6, 9) and C (2, 7, 9) be the vertices of a triangle. The internal bisector of angle A meets BC at point D. Find the coordinates of D.

Show that the three points A (2, 3, 4), B (−1, 2, −3) and C (−4, 1, −10) are collinear and find the ratio in which C divides AB.

The distance of point P (3, 4, 5) from the yz-plane is?