-->

Motion In A Plane

Question
CBSEENPH11018297

Find the angle between the vectors straight A with rightwards arrow on top equals straight A subscript straight x straight i with overparenthesis on top plus straight A subscript straight y straight j with hat on top plus straight A subscript straight z straight k with hat on top and straight B with rightwards arrow on top equals straight B subscript straight x straight i with hat on top plus straight B subscript straight y straight j with hat on top plus straight B subscript straight z straight k with hat on top.

Solution

Let straight theta be the angle between the given two vectors.
Thus, 
                         cos space straight theta space equals space fraction numerator straight A with rightwards arrow on top times straight B with rightwards arrow on top over denominator AB end fraction
Here,                      straight A equals square root of straight A subscript straight x squared plus straight A subscript straight y squared plus straight A subscript straight z squared end root
                               straight B equals square root of straight B subscript straight x squared plus straight B subscript straight y squared plus straight B subscript straight z squared end root
and           <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>
∴      straight theta equals cos to the power of negative 1 end exponent open parentheses fraction numerator straight A subscript straight x straight B subscript straight x plus straight A subscript straight y straight B subscript straight y plus straight A subscript straight z straight B subscript straight z over denominator square root of straight A subscript straight x squared plus straight A subscript straight y squared plus straight A subscript straight z squared end root space square root of straight B subscript straight x squared plus straight B subscript straight y squared plus straight B subscript straight z squared end root end fraction close parentheses, is the angle between the vectors.