the question in 2013 was
Are the unit vectors in cylindrical and spherical coordinate system constant vectors ? expalin .

the answer is
NO , they are not constant .


explanation ,
a vector is constant if
1. its magnitude is constant
2. its direction is constant

all unit vectors have a constant magnitude ie. 1
but to examine if their directions are constant we can use the derivative technique ( as we know that derivative of a constant is zero . so anything constant will generate a zero when we take its derivative )




[Source: Wikipedia]

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