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Find the component of vector space 3 straight i with hat on top minus 4 straight j with hat on top in direction of straight i with hat on top plus straight j with hat on top.


Dot product of two vectors is given by,

               

∴      

New component of  in the direction of 

        

                   

Given,

                and  

Thus,      

          

Magnitude of B,  

So, components of vector in the direction of  

∴             

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If straight A with rightwards arrow on top space equals space straight A subscript straight x straight i with hat on top plus straight A subscript straight y straight j with hat on top plus straight A subscript straight z straight k with hat on top 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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#6 {main}</pre> then find the dot product of straight A with rightwards arrow on top space and space straight B with rightwards arrow on top?


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#6 {main}</pre>

Here, 

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Find the component of vector <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>  in the direction of space space space 12 straight i with hat on top space plus space 5 straight j with hat on top space minus space square root of 126 space straight k with hat on top.


We know 

∴          

Now component of  in the direction of  is,

      

                   

Here,     

and       

Thus,         

and           

                     

∴   

                

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State and prove that dot product is distributive.

Statement: Dot product of a given vector with a sum of number of other vectors is equal to the sum of the dot product of given vector with the other vectors separately.

Statement: Dot product of a given vector with a sum of number of othe


Statement: Dot product of a given vector with a sum of number of othe
                   

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A particle moves in XY plane, such that its position at any instant is
      straight x equals straight alpha space sin space ωt           and       straight y equals straight alpha left parenthesis 1 minus cos space ωt right parenthesis
Find the angle between velocity vector and acceleration vector at any instant.


The position of the particle at any instant is,

       

Therefore the velocity of particle at any instant is,

      

 

Acceleration of particle at any instant is,

      

  

Now,  


       

Since dot product of acceleration vector and velocity vector is zero, therefore the acceleration vector and velocity vector is  

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