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 $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ then find the dot product of $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ ?

Solution

Given that,
$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ 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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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Give two examples of polar vectors.

What are axial vectors?

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