NCERT Solutions Class 11 Chapter 11 Introduction to three dimensional Geometry Exercise 11.1 (original) (raw)

Last Updated : 22 Apr, 2024

Problem 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)

Problem 2: A point is in the XZ-plane. What can you say about its y-coordinate?

**Solution:

If a point is in XZ plane,

**So its y-coordinate is 0

Problem 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:

****(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.

Problem 4: Fill in the blanks:

(i) The x-axis and y-axis taken together determine a plane known as _______.

**Solution:

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 _______.

**Solution:

The coordinates of points in the XY-plane are of the form ****(x, y, 0)**.

(iii) Coordinate planes divide the space into ______ octants.

**Solution:

Coordinate planes divide the space into **eight octants.