## NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry (Ex 12.1) Exercise 12.1

Class 11 Maths NCERT Solutions Chapter 12 Ex 12.1 consistes of all the answers for the chapters of NCERT Class 11 paper - Three Dimensional Geometry. The Exercise 12.1 Class 11 solutions are prepared by some of the best educators in the country. These solutions are simple and ideal for studying. These solutions provide you with a detailed explanation of the entire chapter. You can start your preparation by downloading the Exercise 12.1 Class 11 Maths Solution PDF.

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

Exercise 12.1

Refer to pages 1-3 for exercise 12.1 in the PDF

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

Ans: We know that, the coordinates of any point on the $x$-axis will be as $\left( {x,0,0} \right)$.

Thus, if a point is on the $x$-axis, then its $y$-coordinate will be $0$ and $z$-coordinate will be 0.

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

Ans: We know that, the coordinates of any point in the XZ-plane will be as $\left( {x,0,z} \right)$.

So, in the XZ- plane $y = 0$.

Thus, if a point is in the XZ- plane then the coordinate of $y$will always be 0.

Hence, its $y$-coordinate is 0.

3. Name the octants in which the following points lie:

$\left( {{\mathbf{1,2,3}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( {1,2,3} \right)$ lies in the first octant.

$\left( {{\mathbf{4, - 2,3}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( {4, - 2,3} \right)$ lies in octant IV.

$\left( {{\mathbf{4, - 2, - 5}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( {4, - 2, - 5} \right)$ lies in octant VIII.

$\left( {{\mathbf{4,2, - 5}}} \right)$

Ans: We have the following table,

From the above table, the point $\left( {4,2, - 5} \right)$ lies in octant V.

$\left( {{\mathbf{ - 4,2, - 5}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 4,2, - 5} \right)$ lies in octant VI.

$\left( {{\mathbf{ - 4,2,5}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 4,2,5} \right)$ lies in octant II.

$\left( {{\mathbf{ - 3, - 1,6}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 3, - 1,6} \right)$ lies in octant III.

$\left( {{\mathbf{ - 2, - 4, - 7}}} \right)$

Ans: We have the following table,

Octant Coordinates | I | II | III | IV | V | VI | VII | VIII |

$x$ | + | - | - | + | + | - | - | + |

$y$ | + | + | - | - | + | + | - | - |

$z$ | + | + | + | + | - | - | - | - |

From the above table, the point $\left( { - 2, - 4, - 7} \right)$ lies in octant VII.

4. Fill in the blanks:

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

Ans: In XY-plane, $z = 0$.

Hence, 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 _____________ .

Ans: In XY-plane, $z = 0$.

Let $x$-coordinate be $x$ and $y$-coordinate be $y$.

Hence, the coordinates of points in the XY-plane are of the form $\left( {x,y,0} \right)$.

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

Ans: Coordinate planes divide the space into 8 octants.

## CBSE Solutions for Class 11 Maths Chapter 12 - Introduction to Three Dimensional Geometry Exercise 12.1

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