Dipole - the calc. seems a bit illogical though correct

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exuberant.me
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I was reading the calculation for calculating the electric field due to a dipole at any point P at a distance x from the center of the dipole.

the way they have written the calc. seems a bit illogical

they have broken p into two components pcosθ and psinθ and applied E = kp/r3

Now,


E = Ex + Ey = (kpcosθ)/r3i + (kpsinθ)/r3j

but that would give the net field along some other direction..

it should rather only be

E = Ex = (kpcosθ)/r3

If someone can explain..!
Thanks in advance
 

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i got it cleared at last... actually there was a different problem i faced.. but could not express it here...
btw.. i got it cleared by looking carefully..
they have done the right thing.. for first one it lies on the axial line and for second component it lies on equitorial plane.. i could not focus on this thing... thanks a lot.. !