Can three vectors whose magnitudes are 10, 20 and 25 units lying in plane produce zero resultant?

If the magnitude of any vector lies between sum and difference of the magnitude of other two vectors, and if all the three vectors lay in the same plane, then their resultant can be zero.
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The magnitude of the resultant of stack straight F subscript 1 with rightwards arrow on top space and space stack straight F subscript 2 with rightwards arrow on top is P; If direction of stack straight F subscript 2 with rightwards arrow on top is reversed, the resultant is Q.
Show that
              space straight P squared plus straight Q squared space equals space 2 left parenthesis straight F subscript 1 squared plus straight F subscript 2 squared right parenthesis


Let  be the  angle between two vectors 

∴                    ...(1)

If direction of  is reversed then, then angle between  becomes 

∴           .

                        ...(2)

Adding (1) and (2), we get

              

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If straight A with rightwards arrow on top space and space straight B with rightwards arrow on top are orthogonal , then prove that 
                  open vertical bar straight A with rightwards arrow on top plus straight B with rightwards arrow on top close vertical bar space equals space square root of straight A squared plus straight B squared end root


Magnitude of resultant of two vectors  acting at angle  is given by, 

               

Here,  are orthogonal, therefore  

Therefore, 

             

                       

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The resultant of two vectors straight A with rightwards arrow on top space and space straight B with rightwards arrow on top is <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 perpendicular to stack straight A. with rightwards arrow on top Show that straight B with rightwards arrow on top space equals space square root of 2 open vertical bar straight A with rightwards arrow on top close vertical bar.


Let the angle between  and  be 

Resultant of  is A.

Therefore,

                  

            

             
                           ...(1)

Also resultant is perpendicular to 

∴              

                                                ...(2)

From (1) and (2)

                 

           

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If space space straight R with rightwards arrow on top equals straight A with rightwards arrow on top plus straight B with rightwards arrow on top  and open vertical bar straight R with rightwards arrow on top close vertical bar space equals space open vertical bar straight A with rightwards arrow on top close vertical bar space equals space open vertical bar straight B with rightwards arrow on top close vertical bar then what is the angle between straight A with rightwards arrow on top space and space straight B with rightwards arrow on top ?


Let  be the angle between  

∴ Resultant is given by,

 

 

Hence, R = A = B

Thus,  
     
  

      , is the required angle between them. 

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