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

Topics and Sub Topics in Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry:

 Section Name Topic Name 12 Introduction to Three Dimensional Geometry 12.1 Introduction 12.2 Coordinate Axes and Coordinate Planes in Three Dimensional Space 12.3 Coordinates of a Point in Space 12.4 Distance between Two Points 12.5 Section Formula

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

Question 1: Ans: Question 2: Ans: Question 3: Ans: Question 4: Ans: ### NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.2

Question 1: Ans: Question 2: Ans: Question 3: Ans:   Question 4: Ans: Question 5: Ans: ### NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3

Question 1: Ans: Question 2: Ans: Question 3: Ans: Question 4: Ans: Question 5: Ans: Class 11 Maths NCERT Solutions – Miscellaneous Questions

Question 1: Ans: Question 2: Ans: Question 3: Ans: Question 4: Ans: Question 5: Ans: Question 6: Ans: Exercise 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?

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

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)

(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?

Exercise: 12.2

Q.1: Find the distance between two points whose coordinates are given below:

(i).     (2, 8, 9) and (4, 5, 8)

(ii).    (-3, 4, 5) and (2, 6, -1)

(iii).   (-6, -4, 1) and (5, -2, 6)

(iv).   (-1, 9, 8) and (6, 5, -3)

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

Q.3: Prove the following statements:

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

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

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

Q.4: Find the equation of the set of points P which are equidistant from point  A (3, 2, 1) and point B (-1, 2, 3).

Q.5: The sum of distance of point P from point A (3, 0, 0) and point B (-3, 0, 0) is equal to 12 units. Find the equation of the set of points.

Exercise 12.3

Q.1: Find the coordinates of the point which divides the line segment joining the points (-2, 1, 0) and (1, 3, 6) internally in the ratio of 1:4 and externally in the ratio of 1:4.

Q.2: Given that the points A (3, 2, -4) B (5, 4, -6) and C (9, 8, -10), are collinear. Find the ratio in which line AC is divided by B.

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

Q.4: By using the section formula; Show that the points P (-1, 2, 1), Q (0, 13, 2) and R (2, -3, 4) are collinear.

Q.5: The line segment joining points A (5, 3, -6) and B (9, 15, 7) is trisected by the points P and Q, Find the coordinates of points P and Q.

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