Introduction to 3D Geometry

CBSE Class–11 Mathematics

NCERT Solutions
Chapter - 12 Introduction to Three Dimensional Geometry
Exercise 12.1

1. A point is on the axis. What are its coordinates and coordinates?

Ans. We know that coordinates of any point on the axis will be Therefore, coordinate and coordinate of the point are zero.

2. A point is on XZ-plane. What can you say about its coordinate?

Ans. We know that coordinates of any point in XZ-plane will be Therefore coordinate of the point is zero.

3. Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (– 4, 2, –5), (– 4, 2, 5),(–3, –1, 6) (2, – 4, –7)

Ans. Point (1, 2, 3)lies in I octant

Point (4,-2,3) lies in IV octant

Point (4,-2,-5) lies in VIII octant

Point (4,2,-5) lies in V octant

Point(-4,2,-5) lies in VI octant

Point (-4,2,5) lies in II octant

Point (-3,-1,6) lies in III octant,

Point (2,-4,-7) lies in VII octant

4. Fill in the blanks:

(i) The axis and axis taken together determine a plane known as ____________.

(ii) The coordinates of points in the XY-plane are of the form ____________.

(iii) Coordinates planes divide the space into ____________ octants.

Ans. (i) XY-plane

(ii)

(iii) Eight