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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

8.
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

(i) Distance of P(a, b, c) from XY-plane = $open vertical bar straight c close vertical bar$
∴ Distance of A(2, -3, 4) from XY - plane = $open vertical bar 4 close vertical bar space equals space 4$

(ii) Distance of P(a, b, c) from ZX-plane = $open vertical bar straight b close vertical bar$
∴ Distance of B(4, -3, 1) from ZX-plance = $open vertical bar negative 3 close vertical bar space equals space 3$

(iii) Distance of P(a, b, c) from YZ-plane = $space open vertical bar straight a close vertical bar$
∴ Distance of C (3, -2, -1) from YZ-plane = $open vertical bar 3 close vertical bar equals 3$

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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.

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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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