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Introduction To Three Dimensional Geometry

Fill In the Blanks

The x-axis and y-axis taken together determine a plane known as ____________.

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The coordinates of points in the XY-plane are of the form __________.

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Coordinate planes divide the space into _______ octants.

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Short Answer Type

4. Let P (-2, 3, -4) is a point in space. Find the co-ordinates of the foot of perpendicular from this point to ZX-plane.

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5. Let P (-2, 3, -4) is a point in space. Find the foot of perpendicular from this point to the z-axis.

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6. Let P (-2, 3, -4) is a point in space. Find the the perpendicular distance of P from XY-plane.

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Name the octants in which the following points lie:
A (2, 3, 4), B (6, -3, 3), C (2, -1, -6), D (2, 2, -3), E (-1, 3, -6), F (-1, 3, 3), G (-3, -2,5) and H (-1,-2,-5).

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Long Answer Type

Find the perpendicular distance of:
(i) A (2, -3, 4) from XY-plane
(ii) B (4, -3, 1) from ZX-plane
(iii) C (3, -2, -1) from YZ-plane

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9. The co-ordinates of a point A are (2, -3, 6). Write down the co-ordinates of seven points whose absolute values are the same as those of the co-ordinates of the given point.

The given point is A (2, -3, 6) and has y-co-ordinate negative.
∴ The seven other points are:
(i) B for which all x, y, z are positive
∴ B is (2, 3, 6)
(ii) C for which x is negative, y and z are positive.
∴ C is (-2, 3, 6)
(iii) D for which x, y are positive and z is negative.
∴ D is (2, 3, -6)
(iv) E for which x, y are negative and z is positive.
∴ E is (-2, -3, 6)
(v) F for which x, z are negative and y is positive.
∴ F is (-2, 3, -6)
(vi) G for which x is positive and y, z are negative.
∴ G is (2, -3, -6)
(vii) H for which x, y, z are all negative.
∴ H is (-2, -3, -6)

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Short Answer Type

10. The co-ordinates of a point P are (a, b, c) where a, b, c > 0. If the perpendicular distance of P from XY-plane is equal to half the sum of its perpendicular distances from ZX-plane and YZ-plane, find a relation between a, b and c.

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