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**Exercise 12.1 : ** Solutions of Questions on Page Number : **271**

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**Exercise 12.2 : ** Solutions of Questions on Page Number : **273**

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**Exercise 12.3 : ** Solutions of Questions on Page Number : **277**

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**Exercise Miscellaneous : ** Solutions of Questions on Page Number : **278**

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**Popular Articles**

Q1 :
**
**

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

**Answer :**

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

Answer needs Correction? Click Here

Q2 :
**
**

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

**Answer :**

If a point is in the XZ plane, then its *y*-coordinate is
zero.

Answer needs Correction? Click Here

Q3 :
**
**

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)

**Answer :**

Q4 :
**
**

Fill in the blanks:

**Answer :**

Q1 :
**
**

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)

**Answer :**

Q2 :
**
**

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

**Answer :**

Q3 :
**
**

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.

**Answer :**

Q4 :
**
**

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

**Answer :**

Q5 :
**
**

Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (-4, 0, 0) is equal to 10.

**Answer :**

Q1 :
**
**

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

**Answer :**

Q2 :
**
**

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.

**Answer :**

Q3 :
**
**

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

**Answer :**

Q4 :
**
**

Using section formula, show that the points A (2, â€“3, 4), B (â€“1, 2, 1) and are collinear.

**Answer :**

Q5 :
**
**

Find the coordinates of the points which trisect the line segment joining the points P (4, 2, -6) and Q (10, -16, 6).

**Answer :**

Q1 :
**
**

Three vertices of a parallelogram ABCD are A (3, -1, 2), B (1, 2, -4) andC (-1, 1, 2). Find the coordinates of the fourth vertex.

**Answer :**

Q2 :
**
**

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

**Answer :**

Q3 :
**
**

If the origin is the centroid of the triangle PQR with vertices P
(2*a*, 2, 6), Q (-4, 3*b*,
-10) and R (8, 14, 2*c*), then find the
values of *a*, *b* and *c*.

**Answer :**

Q4 :
**
**

Find the coordinates of a point on *y*-axis which are at a
distance offrom the point P (3,
â€“2, 5).

**Answer :**

Q5 :
**
**

A point R with *x*-coordinate 4 lies on the line segment
joining the pointsP (2, â€“3, 4) and Q (8, 0,
10). Find the coordinates of the point R.

[**Hint** suppose R divides PQ in the ratio *k*: 1. The
coordinates of the point R are given by

**Answer :**

Q6 :
**
**

If A and B be the points (3, 4, 5) and (-1,
3, -7), respectively, find the equation of
the set of points P such that PA^{2} + PB^{2} =
*k*^{2}, where *k* is a constant.

**Answer :**

Maths - Maths : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Introduction to Three Dimensional Geometry ** ( Exercise 12.1, 12.2, 12.3, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Maths : Chapter 3 - Trigonometric Functions Class 11
- Maths : Chapter 4 - Principle of Mathematical Induction Class 11
- Maths : Chapter 5 - Complex Numbers and Quadratic Equations Class 11
- Maths : Chapter 2 - Relations and Functions Class 11
- Maths : Chapter 1 - Sets Class 11
- Maths : Chapter 9 - Sequences and Series Class 11
- Maths : Chapter 6 - Linear Inequalities Class 11
- Maths : Chapter 7 - Permutations and Combinations Class 11
- Maths : Chapter 13 - Limits and Derivatives Class 11
- Maths : Chapter 8 - Binomial Theorem Class 11

Exercise 12.1 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Exercise 12.2 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Exercise 12.3 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Exercise Miscellaneous |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |