NCERT Solutions Class 11th Maths Chapter 12- Introduction to Three Dimensional Geometry Exercise 12.1
| Textbook | NCERT |
| class | Class – 11th |
| Subject | Mathematics |
| Chapter | Chapter – 12 |
| Chapter Name | Introduction to Three Dimensional Geometry |
| grade | Class 11th Maths solution |
| Medium | English |
| Source | last doubt |
NCERT Solutions Class 11th Maths Chapter 12- Introduction to Three Dimensional Geometry Exercise 12.1
?Chapter – 12?
✍Introduction to Three Dimensional Geometry✍
?Exercise 12.1?
1. A point is on the x-axis. What are its y coordinate and z-coordinates?
Solution: If a point is on the x-axis, then the coordinates of y and z are 0.
So the point is (x, 0, 0).
2. A point is in the XZ-plane. What can you say about its y-coordinate?
Solution: If a point is in XZ plane, then its y-co-ordinate is 0.
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).
Solution: Here is the table which represents the octants:
| Octants | I | II | III | IV | V | VI | VII | VIII |
| x | + | – | – | + | + | – | – | + |
| y | + | + | – | – | + | + | – | – |
| z | + | + | + | + | – | – | – | – |
(i) (1, 2, 3)
Here x is positive, y is positive and z is positive.
So it lies in I octant.
(ii) (4, -2, 3)
Here x is positive, y is negative and z is positive.
So it lies in IV octant.
(iii) (4, -2, -5)
Here x is positive, y is negative and z is negative.
So it lies in VIII octant.
(iv) (4, 2, -5)
Here x is positive, y is positive and z is negative.
So it lies in V octant.
(v) (-4, 2, -5)
Here x is negative, y is positive and z is negative.
So it lies in VI octant.
(vi) (-4, 2, 5)
Here x is negative, y is positive and z is positive.
So it lies in II octant.
(vii) (-3, -1, 6)
Here x is negative, y is negative and z is positive.
So it lies in III octant.
(viii) (2, -4, -7)
Here x is positive, y is negative and z is negative.
So it lies in VIII octant.
4. Fill in the blanks:
(i) The x-axis and y-axis taken together determine a plane known as _______.
(ii) The coordinates of points in the XY-plane are of the form _______.
(iii) Coordinate planes divide the space into ______ octants.
Solution:
(i) The x-axis and y-axis taken together determine a plane known as XY Plane.
(ii) The coordinates of points in the XY-plane are of the form (x, y, 0).
(iii) Coordinate planes divide the space into eight octants.