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

Solution

Given,
Here, $straight A with rightwards arrow on top equals straight i with hat on top minus straight j with hat on top plus 2 straight k with hat on top$ , $straight B with rightwards arrow on top space equals space minus 3 straight i with hat on top plus 4 straight j with hat on top minus straight k with hat on top$
∴ $space space space space space space space space space space space space space space space space space space space space space space space space space space straight i with hat on top space space space space space space space space space space space space stack straight j space with hat on top space space space space space space space space space space space space space straight k with hat on top straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space space space space space space space space space space 1 space space space space space space space minus 1 space space space space space space space space space space space space 2 space space space space space space space space space space space space space space space space space space space space space space space minus 3 space space space space space space space space 4 space space space space space space space space space space minus 1$
$space space equals left square bracket left parenthesis negative 1 right parenthesis left parenthesis negative 1 right parenthesis minus left parenthesis 2 right parenthesis left parenthesis 4 right parenthesis right square bracket straight i with hat on top minus left square bracket left parenthesis 1 right parenthesis left parenthesis negative 1 right parenthesis minus left parenthesis 2 right parenthesis left parenthesis negative 3 right parenthesis right square bracket straight j with hat on top$ $plus left square bracket left parenthesis 1 right parenthesis left parenthesis 4 right parenthesis space minus space left parenthesis negative 1 right parenthesis left parenthesis negative 3 right parenthesis right square bracket straight k with hat on top$

$equals negative 7 straight i with hat on top minus 5 straight j with hat on top plus straight k with hat on top$
Now the area of parallelogram formed by vectors $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ is,
$open vertical bar straight A with rightwards arrow on top cross times straight B with rightwards arrow on top close vertical bar space equals space square root of left parenthesis negative 7 right parenthesis squared plus left parenthesis negative 5 right parenthesis squared plus left parenthesis 1 right parenthesis squared end root space equals space square root of 75 space equals space 5 square root of 3$

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

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?

Give two examples of axial vectors.

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