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Introduction To Three Dimensional Geometry

Short Answer Type

41. Find the value of x, so that the point (6, 5, -3) is at a distance of 13 units from the point (x, -7, 0).

95 Views

42. Find the co-ordinates of a point on the z-axis which is equidistant from points A (3, 2, 1) and B (5, 2, 5).

Let the point on z-axis be P (0,0, z).
It is equidistant from A (3, 2, 1) and B (5, 2, 5)
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Using distance formula, we have
$square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared plus left parenthesis straight z minus 1 right parenthesis squared end root space equals space square root of left parenthesis negative 5 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared plus left parenthesis straight z minus 5 right parenthesis squared end root$
$rightwards double arrow$ $square root of straight z squared minus 2 straight z plus 14 end root space equals space square root of straight z squared minus 10 straight z plus 54 end root$
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Hence, the required point is P (0, 0, 5).

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43.

Find points on x - axis which are at a distance of $square root of 29$ units from point A (1, 2, 3).

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44. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and B (3, 2, -1).

102 Views

Long Answer Type

45. Find the equation of set of points P the sum of whose distances from A (4, 0, 0) and B (-4, 0, 0) is equal to 10.

129 Views

Short Answer Type

46. If A and B be the points (3, 4, 5) and (-1, 3, - 7) respectively, find the equation of set of points P such that PA² + PB² = 2k². where k is a constant.

176 Views

47. Find the equation of the locus of a point P or the equation of set of points P which moves so that its distance from A (1, 2, 3) is four times its distance from the YZ-plane.

331 Views

48. Find the distance between the following pairs of points:
(a) A (2, 3, 5), B (4, 3, 1)
(b) A (-3, 7, 2), B (2, 4, - 1)

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49. Show that the following sets of points are collinear.
A (1,2, 3), B (4, 0, 4), C (-2, 4, 2)

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50. Show that the following sets of points are collinear.
P (2, - 4, 1), B (4, 4, 3), C (3, 0, 2)

95 Views