Define cross product of two vectors. Show that cross product of two vectors anti commute. from Physics Motion in A Plane Class 11 Manipur Board
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Define cross product of two vectors. Show that cross product of two vectors anti commute.

Cross product of two vectors is a vector whose magnitude is equal to product of the magnitude of each vector and sine of angle between them and is directed along the normal to the plane containing two vectors. 

              straight A with rightwards harpoon with barb upwards on top space cross times B with rightwards harpoon with barb upwards on top space equals space space A B space sin theta straight c with hat on top

The direction of the cross product of two vectors, that is straight c with hat on top is determined by the right hand screw rule or right hand thumb rule. 

The right hand screw rule states that when you place a screw perpendicular to the plane containing vectors straight A with rightwards harpoon with barb upwards on top space a n d space B with rightwards harpoon with barb upwards on top. Rotate the cap of a screw from straight A with rightwards harpoon with barb upwards on top space t o space B with rightwards harpoon with barb upwards on top to find the direction of straight A with rightwards harpoon with barb upwards on top cross times B with rightwards harpoon with barb upwards on top and <pre>uncaught exception: <b>Http Error #404</b><br /><br />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<br />#0 [internal function]: com_wiris_plugin_impl_HttpImpl_0(Object(com_wiris_plugin_impl_HttpImpl), NULL, 'http://www.wiri...', 'Http Error #404')
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#13 {main}</pre> to find the direction of straight B with rightwards harpoon with barb upwards on top space cross times A with rightwards harpoon with barb upwards on top.

The direction in which the screw will advance gives us the direction of straight c with hat on top.

Therefore, by Right Hand Screw Rule, the direction of straight A with rightwards harpoon with barb upwards on top cross times B with rightwards harpoon with barb upwards on top space a n d space B with rightwards harpoon with barb upwards on top cross times A with rightwards harpoon with barb upwards on top space i s space o p p o s i t e. space

Now, 

                 straight A with rightwards harpoon with barb upwards on top cross times B with rightwards harpoon with barb upwards on top space equals space A B space sin theta space c with hat on top     and

straight B with rightwards harpoon with barb upwards on top cross times A with rightwards harpoon with barb upwards on top space equals space B A space sin theta space stack c space with hat on top

space space space space space space space space space space equals space minus A B space sin theta space stack c space with hat on top

space space space space space space space space space space equals space minus A with rightwards harpoon with barb upwards on top space cross times space B with rightwards harpoon with barb upwards on top 

So, cross product of two vectors anti-commute. 
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