- #1

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why when we transform from cylindrical 2 cartisian or the inverse we take the unit vector in our

consideration and transform it also not just transform the function and relate it to the other

unit vectors ??.

for example : the vector (A= 5 ar + 3π/2 aΦ )

we can say that : r^2 = x^2 + y^2 that's mean that : 25 = x^2 +y^2

and also : x = r cos Φ which means : x= 5 cos 3π/2 so: x = 0

and : y = r sin Φ which means : y= -5

so that our vector will be directly A= -5 ay

but if we did unit vector transformation : ar = cosΦ ax + sinΦ ay

aΦ = -sinΦ ax + cosΦ ay

we will get that : A= -5 ay + π/2 ax

please, I'm so confused in this part and cannot think in it anymore so I just wanna clearance...