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Show that the vector addition follows commutative law.

Let straight A with rightwards arrow on top space and space straight B with rightwards arrow on top be 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)
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#6 {main}</pre> and OQ with rightwards arrow on top comma the two adjacent sides of parallelogram OPSQ.

In the figure, <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)
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#6 {main}</pre> is the diagonal of parallelogram.



Since <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)
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#6 {main}</pre> is equal and parallel to <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)
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#6 {main}</pre>

∴             OP with rightwards arrow on top space equals space QS with rightwards arrow on top space equals space straight A with rightwards arrow on top

Also, space OQ with rightwards arrow on top is equal and parallel to space PS with rightwards arrow on top

∴           OQ with rightwards arrow on top space equals space PS with rightwards arrow on top space equals space straight B with rightwards arrow on top

Now applying triangle law of vector addition to increment OPS comma space we get

             OS with rightwards arrow on top space equals space OP with rightwards arrow on top space plus space PS with rightwards arrow on top space equals space straight A with rightwards arrow on top plus straight B with rightwards arrow on top                ...(1)

Similarly applying triangle law of vector addition to <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)
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#6 {main}</pre> we get

              OS with rightwards arrow on top space equals space OQ with rightwards arrow on top plus QS with rightwards arrow on top space equals space straight B with rightwards arrow on top plus straight A with rightwards arrow on top                ...(2)

From equation (1) and (2),

               space straight A with rightwards arrow on top plus straight B with rightwards arrow on top space equals space straight B with rightwards arrow on top plus straight A with rightwards arrow on top

Hence the vector addition follows commutative law.

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
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Give three examples of scalar quantities.

Mass, temperature and energy
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Give three examples of vector quantities.

Force, impulse and momentum.
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