Class 11 Maths Ncert Solutions Chapter 12 Ex 12.1 Introduction to Three Dimensional Geometry PDF

Class 11 Maths Ncert Solutions Ex 12.1

Class 11 Maths Ncert Solutions Chapter 12 Ex 12.1

For any given point, the sign of its coordinates determines the octant in which it will lie.

Now, from the following table it can be easily determined in which coordinates the point lies.

 

Untitled

 

Q.1: A point is lying on y – axis. What are its ‘x‘ coordinates and ‘z’ coordinates?

Sol.

‘x’ coordinates and ‘z’ coordinates are zero if any point lies on y –axis.

 

Q.2: A point is lying on YZ – plane. What are its ‘x‘ coordinates?

Sol.

If any point lies in the YZ plane then its x-coordinates are zero.

 

Q.3: In which of the octant the following points lie:

(2, 3, 4), (8, -1, -1), (-4, 9, -8), (-1, -2, -3), (4, -5, 6), (7, -1, -4), (-3, -5, 1), (0, 0, -3)

 

Sol.

The x – coordinates, y – coordinates and z – coordinates of point (2, 3, 4) are all positive. Therefore, this point is lying in octant (I).

The x – coordinates, y – coordinates and z – coordinates of point (8, -1, -1) are positive, negative and negative. Therefore, this point is lying in octant (VII).

The x – coordinates, y – coordinates and z – coordinates of point (-4, 9, -8) are negative, positive and negative. Therefore, this point is lying in octant (VI).

The x – coordinates, y – coordinates and z – coordinates of point (-1, -2, -3) are all negative. Therefore, this point is lying in octant (VII).

The x – coordinates, y – coordinates and z – coordinates of point (4, -5, 6) are positive, negative and positive. Therefore, this point is lying in octant (IV).

The x – coordinates, y – coordinates and z – coordinates of point (7, -1, -4) are positive, negative and negative. Therefore, this point is lying in octant (VII).

The x – coordinates, y – coordinates and z – coordinates of point (-3, -5, 1) are negative, negative and positive. Therefore, this point is lying in octant (III).

The x – coordinates, y – coordinates and z – coordinates of point (-1, 2, 2) are negative, positive and positive. Therefore, this point is lying in octant (II).

 

 Q.4: Answer the following questions:

(i). What is the name of a plane determined by the Z-axis and the Y-axis when taken together?

(ii). What is the general form of coordinates of points in the XZ-plane?

(iii). Coordinate plane divides the space into how many octants?

 

Sol.

(i). The plane determined by the Z-axis and the Y-axis when taken together is known as YZ–plane.

(ii). The general form of coordinates of points in the XZ-plane is ( x, 0 , z ).

(iii). The coordinate plane divides the space into 8 octants.

Related Links
Ncert Biology Book Ncert Book Of Class 6Th
Ncert Books For Class 9Th Ncert Class 8 Science Book Pdf
Ncert Class 10 Science Book Ncert Maths Book Class 12 Pdf
Class 12 Maths Ncert Book Ncert Book Of Biology Class 12
Ncert 11Th Biology Book Ncert Physics Book Of Class 11
Ncert Exemplar Problems Solutions Class 10 Ncert Exemplar Solutions