Question

Two vectors acting in opposite direction have resultant 7 units and if they act at angle 90° to each other, the resultant is 13 units. Calculate the magnitude of the two vectors.

Solution

Let A and B be the magnitude of two vectors $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ and let A>B.
When $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ act in opposite direction, the magnitude of resultant is A - B
Now,
A - B = 7 [Given] ...(1)
When $straight A with rightwards arrow on top space and space straight B with rightwards arrow on top$ act perpendicular to each other, then their resultant is,
$square root of straight A squared plus straight B squared end root space equals space 13$
$rightwards double arrow$ $straight A squared plus straight B squared equals 169$ ...(2)
Now, $left parenthesis straight A squared plus straight B squared right parenthesis minus left parenthesis straight A minus straight B right parenthesis squared equals 2 thin space straight A thin space straight B$
∴ $2 AB space equals space 169 minus left parenthesis 7 right parenthesis squared equals 120$
and $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$
$equals 169 plus 120 equals 289$
or $space space straight A plus straight B space equals space 17$ ...(3)
On solving equation (1) and (3), we get
A = 12 and B = 5

For Daily Free Study Material Join wiredfaculty

Motion In A Plane

Two vectors acting in opposite direction have resultant 7 units and if they act at angle 90° to each other, the resultant is 13 units. Calculate the magnitude of the two vectors.

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

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

Two vectors acting in opposite direction have resultant 7 units and if they act at angle 90° to each other, the resultant is 13 units. Calculate the magnitude of the two vectors.

Some More Questions From Motion in A Plane Chapter

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.

What are polar vectors?

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.