Is it possible for a vector to be zero while one component of the vector is not 0?
No. The value of a vector is determined by the square root of
the sum of its components squared. Value= Sqrt(x^2 + y^2 + z^2).
The components of real vectors are real numbers and the square of a
real number is a positive number. The sum of a positive and zeros
is not zero but a positive.
Vectors were created by William Rowan Hamilton in 1843 when he
created Quaternions. Quaternions consist of a real number and three
vector numbers. The vectors are designated by i, j, k where
i^2=j^2=k^2=ijk= -1. The square of a vector is a negative one .
This used to be called an imaginary number. The components of
vectors are real numbers, like v=2i + 3j -5k, the value of v =
sqrt(4 + 9 + 25)=sqrt(38).
Complex numbers are a subset of quaternions involving one vector