Question

is the zero vector parallel to any vector v/

Answer 1

nopes bcoz parallel means the distance inbetween never changes while zero vector is a point and is at a different distance from each segment of the vector

Answer 2

@agent0smith ? ??

Answer 3

@ZakaullahUET has a point. Zero vector is just a point.

Answer 4

how is zero vector a point ? its magnitude is 0

Answer 5

i dont understand http://www.maths.usyd.edu.au/u/MOW/vectors/vectors-4/v-4-2.html it says a is parallel to b if a=kb where k is not 0, but then later it says 0=0b

Answer 6

I think the zero vector is defined as being perpendicular to, and parallel to, every other vector.

Answer 7

@agent0smith u r right, i thought of line but it is vector not line, not just perpendicular and parallel , it is at every angle to another vector

Answer 8

The usual definition excludes the zero vector from being parallel to any other vector ... or being perpendicular. Although if you want, you could define it that way, but honestly it is not very useful.

Answer 9

I think parallel means something more like one vector is a scalar multiple of another, and all vectors can be turned to the zero vector by multiplying the scalar 0 to them.

Answer 10

Isn't the zero vector "technically" orthogonal to any vector? Since the inner product of any vector and zero vector is 0.

Answer 11

^ yeah that's what i was getting at. Dot product and scalar multiples.