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.

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.

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

$\Rightarrow$ 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).

$\Rightarrow$ 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).

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

$\Rightarrow$ 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).

$\Rightarrow$ 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).

$\Rightarrow$ 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).

$\Rightarrow$ 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).

(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.