# Is it possible for a vector to be zero while one component of the vector is not 0?

###### Wiki User

###### 2008-08-26 22:13:52

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

"i".