# 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**

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**NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.2**

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**NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.3**

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**Class 11 Maths NCERT Solutions – Miscellaneous Questions**

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**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)**

** 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?**

**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.**