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A unit vector in xy plane that makes an angle 45 degree with the vector i+j and an angle 60 degree with the vector 3i-4j is

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Solution:    

                    vecp=ahati+b hatjRightarrow left | vecp 
ight |=1Rightarrow a^2+b^2=1.

            Rightarrow      (ahati+bhatj)(hati+hatj)=left | ahati+bhatj 
ight |left | hati+hatj 
ight |cos 45^circ

                        a+b=sqrta^2+b^2	imes sqrt2	imes frac1sqrt2

                        a+b=1               ..........(1)

             Rightarrow        (ahati+bhatj)(3hati-4hatj)=left | ahati+bhatj 
ight |left | 3hati-4hatj 
ight |cos 60^circ

                          3a-4b=5	imes frac12            .......(2)

               Sloving   (1)    and   (2)  We get 

              Hence ,       a=frac1314, b=frac114

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Deependra Verma

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