The absolute value represents a scalar, and the more specific point here is the modulus of a vector. There is no absolute value, and the vector is represented in bold (bold English letters are commonly used in textbooks and papers).

Both bold and vector symbols are scalars.

Specifically, judge for yourself.

1.7

The result of finding r(t) first is wrong.

Because r is a vector. According to the method in the topic, the vector will directly become a scalar (just the module of R vector). In this way, the direction information is lost. This method can only get the correct result if the direction of R remains unchanged. Otherwise, it would be wrong.