  Question

Name the octants in which the following points lie:$$(1, 2, 3), (4, -2, 3) (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7)$$

Solution

The $$x$$-coordinate $$y$$-coordinate and$$z$$-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    MathematicsNCERTStandard XI

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