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Introduction To Three Dimensional Geometry

Short Answer Type

11. Find the locus of a point P (x, y, z), where x > y > z > 0, such that its distance from ZX-plane exceeds ¹/₂ the sum of its distances from XY-plane and YZ-plane by 2.

The point is P(x, y, z), where x, y, z>0
Distance from ZX-plane = $space space open vertical bar straight y close vertical bar space equals space straight y$
Distance from XY-plane = $open vertical bar straight z close vertical bar equals straight z$
Distance from YZ-plane = $open vertical bar straight x close vertical bar equals straight x$
According to the question, we have
$space space space space space space space space space straight y minus 1 half left parenthesis straight z plus straight x right parenthesis equals 2$
$rightwards double arrow$ 2y - z - x = 4
Hence, the locus is x - 2y + z + 4 =0

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12.

Find the octant in which the following points lie:
A (-3,1, 2), B (-3, 1, -2), C (-3, -1,-2), D (3, -1, -2) and E (3,1, 2).

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13. A point lies on the x-axis at a distance of 5 units towards OX'. What are its co-ordinates?

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14. A point lies on z-axis at a distance of 3 units in the direction OZ. Write its co-ordinates.

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15. A point lies on y-axis and is at a distance of 4 units in the direction OY'. Write its co-ordinates.

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16. A point lies on XY-plane with distances 4 units along OX and 3 units along OY. Write its co-ordinates.

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17. A point lies on YZ-plane with distances 4 units along OY and 5 units along OZ'. Write its co-ordinates.

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18. A point lies on ZX-plane with distances 3 units along OX' and 5 units along OZ'. Write its co-ordinates.

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19.

Find the perpendicular distance of point A (-3, 2, -4) from:
(a) ZX-plane (b)XY-plane (c) YZ-plane.

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Long Answer Type

20. The co-ordinates of a point A are (-2, 1, -7). Find the co-ordinates of 7 other points B, C, D, E, F, G and H whose co-ordinates have the same absolute values as those of the co-ordinates of point A.