If straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space straight C with rightwards arrow on top cross times straight B with rightwards arrow on top, the do you think that A is necessarily equal to C?



Here,   
Let the angle between  be  and that between  be .

∴            


           

and             


Therefore,
                  


                     


Now,   

and           then 


Thus, A is not necessarily equal to C.

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Show that:
left parenthesis straight A with rightwards arrow on top minus straight B with rightwards arrow on top right parenthesis cross times left parenthesis straight A with rightwards arrow on top plus straight B with rightwards arrow on top right parenthesis space equals space 2 left parenthesis straight A with rightwards arrow on top cross times straight B with rightwards arrow on top right parenthesis

L.H.S. =  

          

       
 
         = R.H.S.

Hence, proved. 

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If diagonals of a parallelogram are straight P with rightwards arrow on top space and space straight Q with rightwards arrow on top comma then find the area of the parallelogram.


Let the sides of the parallelogram be straight A with rightwards arrow on top space and space straight B with rightwards arrow on top whose diagonals are straight P with rightwards arrow on top space and space stack straight Q. with rightwards arrow on top
        
Let the sides of the parallelogram be  whose diagonals are     ?

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Find the unit vector perpendicular to both the vectors given below:
straight P with rightwards arrow on top space equals left parenthesis 3 straight i with hat on top minus 2 straight j with hat on top plus 4 straight k with hat on top right parenthesis  and  <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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The unit vector perpendicular to vectors  is given by,

                     
We have,

                  

and             

Therefore,
               

and       

∴           , is the required unit vector. 

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What is the angle between straight A with rightwards arrow on top plus straight B with rightwards arrow on top space and space straight B with rightwards arrow on top cross times straight A with rightwards arrow on top ?


Vector straight A with rightwards arrow on top cross times straight B with rightwards arrow on top is perpendicular to the plane containing straight A with rightwards arrow on top space and space straight B with rightwards arrow on top.
          straight A with rightwards arrow on top plus straight B with rightwards arrow on top is the resultant of <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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therefore lies in the plane containing straight A with rightwards arrow on top space and space straight B with rightwards arrow on top.
∴  Angle between straight A with rightwards arrow on top cross times straight B with rightwards arrow on top and straight A with rightwards arrow on top plus straight B with rightwards arrow on top is 90 degree.
Alternatively:   

Vector  is perpendicular to the plane containing           ?

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