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If straight A with rightwards arrow on top space equals space straight A subscript straight x straight i with hat 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 <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> then find the dot product of straight A with rightwards arrow on top space and space straight B with rightwards arrow on top?


Given that,

            <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> and 

           straight B with rightwards harpoon with barb upwards on top space equals space B subscript x i with hat on top space plus space B subscript y space j with hat on top space plus space B subscript z space k with hat on top
Therefore, 

straight A with rightwards harpoon with barb upwards on top. straight B with rightwards harpoon with barb upwards on top space equals space left parenthesis straight A subscript straight x straight i with hat on top space plus space straight A subscript straight y space straight j with hat on top space plus space straight A subscript straight z straight k with hat on top right parenthesis space. space left parenthesis straight B subscript straight x straight i with hat on top space plus space straight B subscript straight y straight j with hat on top space plus space straight B subscript straight z straight k with hat on top right parenthesis space

space space space space space space space space equals space straight A subscript straight x straight B subscript straight x space left parenthesis straight i with hat on top. straight i with hat on top right parenthesis space plus space straight A subscript straight y straight B subscript straight x space left parenthesis straight j with hat on top. straight i with hat on top right parenthesis space plus space straight A subscript straight z straight B subscript straight x space left parenthesis straight k with hat on top space. straight i with hat on top right parenthesis space plus

space space space space space space space space space space space space straight A subscript straight x straight B subscript straight y space left parenthesis straight i with hat on top. straight j with hat on top right parenthesis space plus space straight A subscript straight y straight B subscript straight y space left parenthesis straight j with hat on top. straight j with hat on top space right parenthesis plus space straight A subscript straight z straight B subscript straight y space left parenthesis straight k with hat on top space. straight j with hat on top right parenthesis space space plus

space space space space space space space space space space space straight A subscript straight x straight B subscript straight z space left parenthesis straight i with hat on top. straight k with hat on top right parenthesis plus space straight A subscript straight y straight B subscript straight z space left parenthesis straight j with hat on top. straight k with hat on top right parenthesis space plus space straight A subscript straight z straight B subscript straight z space left parenthesis straight k with hat on top space. straight k with hat on top right parenthesis space

We space have comma space

space left parenthesis straight i with hat on top. straight i with hat on top right parenthesis space equals space left parenthesis straight j with hat on top. straight j with hat on top space right parenthesis space equals space left parenthesis straight k with hat on top space. straight k with hat on top right parenthesis space equals space 1 space and space

left parenthesis straight j with hat on top. straight i with hat on top right parenthesis space equals left parenthesis straight i with hat on top. straight j with hat on top right parenthesis space equals space 0

left parenthesis straight k with hat on top space. straight i with hat on top right parenthesis space equals space space equals space 0

left parenthesis straight k with hat on top space. straight j with hat on top right parenthesis space equals left parenthesis straight j with hat on top. straight k with hat on top right parenthesis space equals space 0 space

Therefore comma space

straight A with rightwards harpoon with barb upwards on top. space straight B with rightwards harpoon with barb upwards on top space equals space straight A subscript straight x straight B subscript straight x space plus space straight A subscript straight y straight B subscript straight y space plus space straight A subscript straight z straight B subscript straight z

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Give three examples of scalar quantities.

Mass, temperature and energy
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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


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