Class 12MathematicsTHREE DIMENSIONAL GEOMETRYSystem of co-ordinates, Direction cosines and direction ratios, Projection
EasyName the octants in which the following points lie:
$(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (-2, -4, -7)$
$(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (-2, -4, -7)$
The octants are determined by the signs of the coordinates $(x, y, z)$:
$1$. $(1, 2, 3)$: All positive,so it lies in octant $I$.
$2$. $(4, -2, 3)$: $(+, -, +)$,so it lies in octant $IV$.
$3$. $(4, -2, -5)$: $(+, -, -)$,so it lies in octant $VIII$.
$4$. $(4, 2, -5)$: $(+, +, -)$,so it lies in octant $V$.
$5$. $(-4, 2, -5)$: $(-, +, -)$,so it lies in octant $VI$.
$6$. $(-4, 2, 5)$: $(-, +, +)$,so it lies in octant $II$.
$7$. $(-3, -1, 6)$: $(-, -, +)$,so it lies in octant $III$.
$8$. $(-2, -4, -7)$: $(-, -, -)$,so it lies in octant $VII$.
$1$. $(1, 2, 3)$: All positive,so it lies in octant $I$.
$2$. $(4, -2, 3)$: $(+, -, +)$,so it lies in octant $IV$.
$3$. $(4, -2, -5)$: $(+, -, -)$,so it lies in octant $VIII$.
$4$. $(4, 2, -5)$: $(+, +, -)$,so it lies in octant $V$.
$5$. $(-4, 2, -5)$: $(-, +, -)$,so it lies in octant $VI$.
$6$. $(-4, 2, 5)$: $(-, +, +)$,so it lies in octant $II$.
$7$. $(-3, -1, 6)$: $(-, -, +)$,so it lies in octant $III$.
$8$. $(-2, -4, -7)$: $(-, -, -)$,so it lies in octant $VII$.
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