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Motion In A Plane

Question
CBSEENPH11018239
Wired Faculty App

Resolve the rectangular components of a vector in three dimensions?

Solution

Let us resolve the rectangular components of a vector straight R with rightwards arrow on top represented by <pre>uncaught exception: <b>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</b><br /><br />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<br />#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> in three dimensions.
                
From point P, draw a perpendicular PM on XY plane and from M draw a perpendicular PM on XY plane and from M draw perpendicular ML on Y axis and MK on X axis. '
Using triangle law to increment OKM comma
OM with rightwards harpoon with barb upwards on top space equals space OK with rightwards harpoon with barb upwards on top space plus KM with rightwards harpoon with barb upwards on top space space space space space space space space space... thin space left parenthesis 1 right parenthesis Using space triangle space law space to space increment OMP comma OP with rightwards harpoon with barb upwards on top space equals space OM with rightwards harpoon with barb upwards on top space plus space MP with rightwards harpoon with barb upwards on top space space space space space space space space space space space... space left parenthesis 2 right parenthesis space From space equation space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space stack OP space with rightwards harpoon with barb upwards on top space equals space OK with rightwards harpoon with barb upwards on top space plus KM with rightwards harpoon with barb upwards on top space space plus MP with rightwards harpoon with barb upwards on top Here comma space vector space OK with rightwards harpoon with barb upwards on top space comma space KM with rightwards harpoon with barb upwards on top space and space MP with rightwards harpoon with barb upwards on top space are space mutually space perpendicular space to space each space other. space Therefore comma space vectors space OK with rightwards harpoon with barb upwards on top space comma space KM with rightwards harpoon with barb upwards on top space and space MP with rightwards harpoon with barb upwards on top space are space called space rectangular space components space of space vector space straight R with rightwards harpoon with barb upwards on top. space Now comma space straight X comma space straight Y space and space straight Z space components space are space represented space by space straight R with rightwards harpoon with barb upwards on top subscript straight x comma space straight R with rightwards harpoon with barb upwards on top subscript straight y space and space straight R with rightwards harpoon with barb upwards on top subscript straight z space respectively. Unit space vectors space along space straight X comma space straight Y space and space straight Z space axis space are space straight i with hat on top comma space straight j with hat on top space and space straight k with hat on top. So comma space resultant space is space given space by comma space straight R with rightwards harpoon with barb upwards on top space equals space stack straight R subscript straight x with rightwards harpoon with barb upwards on top space plus space stack straight R subscript straight y with rightwards harpoon with barb upwards on top space plus space space stack straight R subscript straight z with rightwards harpoon with barb upwards on top space If space vector space straight R with rightwards harpoon with barb upwards on top space space has space magnitude space straight R space and space makes angle space straight theta subscript straight x comma space straight theta subscript straight y space and space straight theta subscript straight z comma space with space positive space direction space of space straight X comma space straight Y space and space straight Z space axis space respectively comma space then OK space equals space straight R subscript straight x space equals space straight R space space cos space straight theta subscript straight x KM space equals space straight R subscript straight y space equals space straight R space sin space space straight theta subscript straight y MP space equals space space straight R subscript straight z space equals space straight R space sin space space straight theta subscript straight z Thus comma space straight R with rightwards harpoon with barb upwards on top space equals space straight R subscript straight x straight i with hat on top space plus space straight R subscript straight y straight j with hat on top space plus space straight R subscript straight z straight k with hat on top space space space space space space space space equals space space space Rcos space straight theta subscript straight x space straight i with hat on top plus straight R space sin space space straight theta subscript straight y straight j with hat on top space plus straight R space sin space space straight theta subscript straight z straight k with hat on top
The above expression gives us the rectangular components of a vector in three dimension. 
               

Some More Questions From Motion in A Plane Chapter

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.

What are tensors?

Give one example of tensor.

What is module of vector?

What are equal vectors?

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