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#6 {main}</pre> and straight B with rightwards arrow on top space equals space 2 straight i with hat on top plus straight j with hat on top minus 4 straight k with hat on top?


Given that,

           

and      

Let straight theta be the angle between the given two vectors.

We know,  

∴               

Now           

                         

Magnitude is given by,

 



 Thus, angle between the vectors,

 

                   

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#6 {main}</pre> and straight B with rightwards arrow on top space equals space minus 4 straight i with hat on top plus 2 straight j with hat on top are perpendicular to each other.


Given,       

and            

  have to be perpendicular to each other.

To prove that we will find the dot product.

  

         

Hence     

Since, the dot product is zero the two vectors are perpendicular to each other. 

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A particle moves from point (2, 3, 5) to (8, -4, 2) when a force of 3 straight i with hat on top minus 7 straight j with hat on top minus straight k with hat on top unit is applied on it. Find the work done by the force.


Given, a particle moves from point P(2,3,5) to Q(8,-4,2). 

Force applied on th particle, F =  

Therefore, the displacement undergone by the particle is, 
              

                 

Therefore work done by force is, 

  

               J

 

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For what value of c the vector 2 straight i with hat on top plus straight c straight j with hat on top will be perpendicular to:
(i) Z-axis      (ii) Y-axis?


(i) Vector  is zero.

i.e.                       

                  

                     

The equation is satisfied for all values of c.

Therefore  is always perpendicular to Z-axis whatever the value of c.

(ii) Similarly        

                    

                            

                                    

∴   is perpendicular to Y-axis if c = 0.

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#6 {main}</pre>


Here,    

Therefore the magnitude of vector 

 

      

Now the unit vector in direction of  is, 

     

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