Question

Find the magnitude and direction of resultant of two vectors without using the parallelogram of vector addition.

Solution

Let $space straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top$ be two vectors acting at angle $straight theta$ .
$straight R with rightwards harpoon with barb upwards on top space$ is the resultant of $straight P with rightwards harpoon with barb upwards on top space a n d space Q with rightwards harpoon with barb upwards on top$ .
Therefore, $straight R with rightwards harpoon with barb upwards on top space equals space P with rightwards harpoon with barb upwards on top space plus space Q with rightwards harpoon with barb upwards on top$

$<pre>uncaught exception: Http Error #404 in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php line 61 #0 [internal function]: com_wiris_plugin_impl_HttpImpl_0(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Http Error #404') #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('com_wiris_plugi...', Array) #2 [internal function]: _hx_lambda->execute('Http Error #404') #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(532): call_user_func_array(Array, Array) #4 [internal function]: haxe_Http_5(true, Object(com_wiris_plugin_impl_HttpImpl), Object(com_wiris_plugin_impl_HttpImpl), Array, Object(haxe_io_BytesOutput), true, 'Http Error #404') #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/php/Boot.class.php(769): call_user_func_array('haxe_Http_5', Array) #6 [internal function]: _hx_lambda->execute('Http Error #404') #7 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(27): call_user_func_array(Array, Array) #8 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(444): com_wiris_plugin_impl_HttpImpl->onError('Http Error #404') #9 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/haxe/Http.class.php(458): haxe_Http->customRequest(true, Object(haxe_io_BytesOutput), NULL, NULL) #10 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/HttpImpl.class.php(40): haxe_Http->request(true) #11 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(80): com_wiris_plugin_impl_HttpImpl->request(true) #12 /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) #13 {main}</pre>$
Let, the resultant $straight R with rightwards harpoon with barb upwards on top$ make angle $straight alpha$ with $OA with rightwards harpoon with barb upwards on top$ .
$straight R with rightwards harpoon with barb upwards on top. P with rightwards harpoon with barb upwards on top space equals space stack left parenthesis P with rightwards harpoon with barb upwards on top space plus Q with rightwards harpoon with barb upwards on top right parenthesis space. space P with rightwards harpoon with barb upwards on top R P space cos space alpha space equals space P with rightwards harpoon with barb upwards on top. P with rightwards harpoon with barb upwards on top space plus space Q with rightwards harpoon with barb upwards on top. P with rightwards harpoon with barb upwards on top R P thin space cos space alpha space equals space P squared space plus space P Q space cos theta space space space space space space space space space space space space space space... space left parenthesis 1 right parenthesis space$
Also,
$open vertical bar straight R with rightwards harpoon with barb upwards on top cross times straight P with rightwards harpoon with barb upwards on top close vertical bar space equals space open parentheses P with rightwards harpoon with barb upwards on top plus Q with rightwards harpoon with barb upwards on top close parentheses cross times P with rightwards harpoon with barb upwards on top space R P space sin space alpha space equals space open vertical bar P with rightwards harpoon with barb upwards on top cross times P with rightwards harpoon with barb upwards on top space plus space Q with rightwards harpoon with barb upwards on top cross times P with rightwards harpoon with barb upwards on top close vertical bar R P space cos alpha space equals space P Q space sin space theta space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis space D i v i d i n g space e q u a t i o n space left parenthesis 2 right parenthesis space b y space left parenthesis 1 right parenthesis comma space w e space h a v e fraction numerator R P space sin alpha over denominator R P space cos space alpha end fraction space equals space fraction numerator P Q space sin space theta over denominator P squared space plus space P Q space cos theta end fraction space i. e. comma space tan alpha space equals space fraction numerator Q space sin theta over denominator P space plus space Q cos theta end fraction space space space space space space space space space space$
Thus, for two vectors acting in the same direction, the magnitude of the resultant vector is equal to the sum of the magnitude of two vectors and acts along the direction of $straight A with rightwards harpoon with barb upwards on top space a n d space B with rightwards harpoon with barb upwards on top.$

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Find the magnitude and direction of resultant of two vectors without using the parallelogram of vector addition.

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Find the magnitude and direction of resultant of two vectors without using the parallelogram of vector addition.

Some More Questions From Motion in A Plane Chapter

What is a vector quantity?

Give three examples of scalar quantities.

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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.