# NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

## NCERT Solutions Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Pdf

The NCERT Solutions for Class 11 Maths Chapter 11: Conic Sections, Exercise 12.2, have been meticulously prepared by experts at Physics Wallah to help students score higher. You can download and share these comprehensive NCERT Class 11 Maths solutions from Physics Wallah.

### NCERT Solutions for Class 11Maths chapter 12 Exercise 12.1

### EX 12.1 Class 11 Maths Question 1:

A point is on the x-axis. What are its y- coordinates and z coordinates?

**Ans:**

If a point is on the x-axis, then its y-coordinates and z-coordinates are zero.

### EX 12.1 Class 11 Maths Question 2:

A point is on the xz-plane. What can you say about its y-coordinate?

**Ans:**

If a point is on the xz-plane, then its y-coordinate is zero.

### EX 12.1 Class 11 Maths Question 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:**

The x –coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I.

The x –coordinate, y-coordinate, and z-coordinate of point (4, -2, 3) are all positive. Therefore, this point lies in octant IV

The x –coordinate, y-coordinate, and z-coordinate of point (4, -2, -5) are all positive. Therefore, this point lies in octant VIII.

The x –coordinate, y-coordinate, and z-coordinate of point (4, 2, -5) are all positive. Therefore, this point lies in octant V.

The x –coordinate, y-coordinate, and z-coordinate of point (-4, 2, -5) are all positive. Therefore, this point lies in octant VI.

The x –coordinate, y-coordinate, and z-coordinate of point (-4, 2, 5) are all positive. Therefore, this point lies in octant II.

The x –coordinate, y-coordinate, and z-coordinate of point (-3, -1, 6) are all positive. Therefore, this point lies in octant III.

The x –coordinate, y-coordinate, and z-coordinate of point (2, -4, -7) are all positive. Therefore, this point lies in octant VIII.

### EX 12.1 Class 11 Maths Question 4:

Fill in the blanks;

**Ans:**

(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) Coordinates planes divide the space into eight octants.

## NCERT Solutions for Class 11Maths chapter 12 Exercise 12.2

### EX 12.2 Class 11 Maths Question 1:

Find the distance between the following pairs of points:

(i) (2, 3, 5,) and (4, 3, 1,) (ii) (-3, 7, 2,) and (2, 4, -1,)

(iii) (-1, 3, -4,) and (1, -3, 4,) (iv) (2, -1, 3,) and (-2, 1, 3,)

**Ans:**

The distance between points P(x_{1}, y_{1}, z_{1}) and P (x_{2}, y_{2},z_{2}) is given by

### EX 12.2 Class 11 Maths Question 2:

Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.

**Ans:**

Let points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) be denoted by P, Q, and R respectively,

Points P, Q, and R are collinear if they lie on a line.

### EX 12.2 Class 11 Maths Question 3:

Verify the following:

(i) (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle.

(ii) (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled triangle.

(iIi) (-1, 2, 1), (1, -2, 5) (4, -7, 8) and (2, -3, 4) are the vertices of a parallelogram.

**Ans:**

(i) Let points (0, 7, -10), (1, 6, -6) and (4, 9, -6) be denoted by A, B, and C respectively.

### EX 12.2 Class 11 Maths Question 4:

Find the equation of the set of point which are equidistant from the points (1, 2, 3) and (3, 2, -1)

**Ans:**

Let P (x, y, z) be the point that is equidistant from points A(1, 2, 3) and B(3, 2, -1). Accordingly, PA = PB

## NCERT Solutions for Class 11Maths chapter 12 Exercise 12.3

### EX 12.3 Class 11 Maths Question 1:

Find the coordinates of the point which divides the line segment joing the points(-2, 3, 5) and (1, -4, 6) in the ratio (i) 2:3 externally.

**Ans:**

(i) The coordinates of point R that divides the line segment joining points P (x _{1}, y_{1}, z_{1}) and Q (x_{2}, y_{2}, z_{2}) internally in the ratio m:n are

### EX 12.3 Class 11 Maths Question 2:

Given that P (3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR.

**Ans:**

Let Point Q(5, 4, -6) divide the line segment joining points P (3, 2, -4) and R(9, 8, -10) in the ratio k:1.

Therefore, by section formula,

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).

**Ans:**

Let the YZ planedivied the line segment joining points (-2, 4, 7) and (3, -5, 8) in the ratio k:1.

Hence, by section formula, the coordinates of point of intersection are given

## Class 11 Maths NCERT Solution- Miscellaneous Quetions

### Miscellaneous Exercise Class 11 Maths Question 1:

Three vertices of a paralle logram ABCD are A (3, -1, 2), B (1, 2, -4) and C(-1, 1, 2). Find the coordinates of the fourth vertex.

**Ans:**

The three vertices of a parallelogram ABCD are as A (3, -1, 2), B (1, 2, -4) and C(-1, 1, 2). Let the coordinates of the fourth vertex be D (x, y, z).

### Miscellaneous Exercise Class 11 Maths Question 2:

Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).

**Ans:**

Let AD, BE and CF be the medians of the given triangle ABC.