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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).

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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).

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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).

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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.

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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.

Let one of the points be P(x, y, z)
A (3, 4 5) and B (-1, 3, -7) be two given points
The given condition is: $space space PA squared plus PB squared space equals space 2 straight k squared$ ...(i)
Using distance formula, we have $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
$PB space equals space square root of left parenthesis straight x plus 1 right parenthesis squared plus left parenthesis straight y minus 3 right parenthesis squared plus left parenthesis straight z plus 7 right parenthesis squared end root$
∴ From (i), we have
$left square bracket left parenthesis straight x minus 3 right parenthesis squared plus left parenthesis straight y minus 4 right parenthesis squared plus left parenthesis straight z minus 5 right parenthesis squared right square bracket space plus space left square bracket left parenthesis straight x plus 1 right parenthesis squared plus left parenthesis straight y minus 3 right parenthesis squared plus left parenthesis straight z plus 7 right parenthesis squared right square bracket space equals space 2 straight k squared$
$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
Hence, the equation of set of points P is $2 straight x squared plus 2 straight y squared plus 2 straight z squared minus 4 straight x minus 14 straight y plus 4 straight z plus 109 minus 2 straight k squared equals 0$

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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.

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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)

106 Views

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

99 Views

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

95 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

Long Answer Type

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.

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.