Consider the following table.

Octants | I | II | III | IV | V | VI | VII | VIII |

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

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

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

By following rules given in the above table, we can conclude the following results.

Since, all the three coordinates in the point (1,2,3) are positive, so this point is in the octant I .

Since in the point (4,−2,3) , the x and z -coordinate are positive and the y - coordinate is negative, so this point is in the octant IV.

Since in the point (4,−2,−5) , the y and z -coordinate are negative and the x - coordinate is positive, so this point is in the octant VIII .

Since in the point (4,2,−5) , the x and y-coordinate are positive and the z - coordinate is negative, so this point is in the octant V.

Since in the point (−4,2,−5) , the x and z -coordinate are negative and the ycoordinate is positive, so this point is in the octant VI.

Since in the point (−3,−1,6) , the x and y-coordinate are negative and the z - coordinate is positive, so this point is in the octant II .

Since in the point (−2,−4,−7) , all the three coordinates in the point are negative, so this point is in the octant VII .

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