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Question

# 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)

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Solution

## The x-coordinate y-coordinate andz-coordinate of point (1,2,3) are all positive.Therefore this point lies in octant IThe x-coordinate y-coordinate and z-coordinate of point (4,−2,3) are positivenegative and positive respectively. Therefore this point lies in octant IVThe x-coordinate y-coordinate and z-coordinate of point (4,−2,−5) are positivenegative and negative respectively. Therefore this point lies in octant VIIIThe x-coordinate, y-coordinate and z-coordinate of point (4,2,−5) are positivepositive and negative respectively. Therefore this point lies in octant VThe x-coordinate, y-coordinate and z-coordinate of point (−4,2,−5) are negativepositive, and negative respectively. Therefore this point lies in octant VIThe x-coordinate, y-coordinate and z-coordinate of point (−4,2,5) are negativepositive and positive respectively. Therefore this point lies in octant IIThe x-coordinate y-coordinate and z-coordinate of point (−3,−1,6) are negativenegative and positive respectively. Therefore this point lies in octant IIIThe x-coordinate, y-coordinate and z-coordinate of point (2,−4,−7) are positivenegative and negative respectively. Therefore this point lies in octant VIII

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