Question

Fun vector question!

Answer 1

\[\Large \bar a \cdot \bar b = 0 \] Is it possible for a vector c to be parallel to both a and b?

Answer 2

vector a and b are perpendicular in this case..

Answer 3

vector c can be parallel to any one of vectors a and b..

Answer 4

But not both simultaneously, This is my judgement.. :P

Answer 5

Suppose we are in R^2 then if we have\[\Large \bar a \cdot \bar z=0\] this implies that z is perpendicular to a, so that means it has to be parallel to b. But it turns out \[\Large \bar b \cdot \bar z = 0\] z is perpendicular to b so it is also parallel to a!

So if c is the zero vector, it is both parallel and perpendicular to every vector haha. =P