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Sequences And Series

Question
CBSEENMA11014970
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Verify the following : (0, 7, -10), (1, 6, -6) and ( 4, 9, -6) are the vertices of an isosceles triangle.

Solution
straight A left parenthesis 0 comma space 7 space minus 10 right parenthesis left right arrow left parenthesis straight x subscript 1 comma space straight y subscript 1 comma space straight z subscript 1 right parenthesis straight B left parenthesis 1 comma space 6 comma space minus 6 right parenthesis left right arrow left parenthesis straight x subscript 2 comma space straight y subscript 2 comma space straight z subscript 2 right parenthesis straight C left parenthesis 4 comma space 9 comma space minus 6 right parenthesis left right arrow left parenthesis straight x subscript 3 comma space straight y subscript 3 comma space straight z subscript 3 right parenthesis
Using distance formula, we have
     <pre>uncaught exception: <b>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</b><br /><br />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<br />#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>
                   equals space square root of left parenthesis negative 1 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared end root space equals space square root of 18 space equals space 3 square root of 2
             BC equals square root of left parenthesis straight x subscript 2 minus straight x subscript 3 right parenthesis squared plus left parenthesis straight y subscript 2 minus straight y subscript 3 right parenthesis squared plus left parenthesis straight z subscript 2 minus straight z subscript 3 right parenthesis squared end root
                  equals space square root of left parenthesis negative 3 right parenthesis squared plus left parenthesis negative 3 right parenthesis squared plus left parenthesis 0 right parenthesis squared end root space equals space square root of 18 space equals space 3 square root of 2
             CA space equals space square root of left parenthesis straight x subscript 3 minus straight x subscript 1 right parenthesis squared plus left parenthesis straight y subscript 3 minus straight y subscript 1 right parenthesis squared plus left parenthesis straight z subscript 3 minus straight z subscript 1 right parenthesis squared end root
                   equals square root of left parenthesis 4 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis 4 right parenthesis squared end root space equals space square root of 36 space equals space 6
rightwards double arrow       AB equals BC not equal to CA
Hence, <pre>uncaught exception: <b>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</b><br /><br />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<br />#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> is an isosceles triangle.

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Some More Questions From Sequences and Series Chapter

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

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

Coordinate planes divide the space into _______ octants.

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.

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

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

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).

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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