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

Dear vikas

let vector b ai+bj

a.1+b.1 = 1*(2^0.5).cos45

= a+b =1

and a^2+b^2 = 1

=>(a+b)^2 - a^2-b^2 = 0

=>2ab = 0

so a=0 or b=0

so a=1,b=0

or a=0,b=1

a.3-b.4 = 5*cos60

=>3a-4b =5/2

either a=1 or b=1 doesnt suit.So there is no vector in xy-plane which satisfies given conditions

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Prudhvi Teja

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