Question

At what angle do the two vectors of magnitude A + B and A - B act so that their resultant is $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ ?

Solution

The magnitude of the resultant of two vectors $space straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top$ acting at angle $straight theta$ is given by,
   $space space straight R equals square root of straight P squared plus straight Q squared plus 2 PQcosθ end root$
Here, P = A + B, Q = A - B
$R e s u l t a n t space comma space straight R space equals space square root of 3 straight A squared plus straight B squared end root therefore space P Q space equals space straight A squared space minus space straight B squared P u t t i n g space t h e space v a l u e s space o f space straight P comma space straight Q comma space straight R space a n d space P Q space i n space a b o v e space e q u a t i o n comma space square root of 3 straight A squared plus straight B squared end root space equals space square root of left parenthesis straight A plus straight B right parenthesis squared plus left parenthesis straight A minus straight B right parenthesis squared plus 2 left parenthesis straight A squared minus straight B squared right parenthesis space c o s theta end root T a k i n g space s q u a r e space o n space b o t h space s i d e s comma space space space space space space space space 3 straight A squared space plus space straight B squared space equals space left parenthesis straight A plus straight B right parenthesis squared space plus space left parenthesis straight A minus straight B right parenthesis squared space plus 2 space left parenthesis straight A squared minus straight B squared right parenthesis c o s theta rightwards double arrow space space straight A squared space minus space straight B squared space equals 2 space left parenthesis straight A squared minus straight B squared right parenthesis c o s theta T h a t space i s comma space c o s space straight theta space equals space bevelled 1 half rightwards double arrow space straight theta space equals space 60 to the power of 0$

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Motion In A Plane

Some More Questions From Motion in A Plane Chapter

Give three examples of vector quantities.

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.

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