If lal= 2, lbl= 3 and a.b= √11 then laxbl = ?

 

If lal= 2, lbl= 3 and a.b= √11 then laxbl = ? 

Answer :- a.b = |a||b| cos (theta) 

          or, √11 = 2x3 cos (theta)             

         or, √11/6 = cos (theta) 

           or, √11/6 = √(1-sin²(theta))

              S.B.S (squaring on both side)

              or, 11/36 = 1 - sin²(theta)

           or, sin²(theta) = (36-11)/3

             or, sin²(theta) = 25/36

              .'. sin(theta) = 5/6

Now, |axb| = |a||b| sin(theta)

                    = 2x3x5/6

                     = 5 

          .'. |axb| = 5   

                                     

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