My question is:
Lets say I have a unit vector a that is orthogonal to the vector p $<4,5>$. If I scale a by a scalar 't', then I have a general vector that is perpendicular to the p. This seems that the set of all the vectors that are obtained by scaling the unit vector can lie on a single line, which means the solution is a line.
But in the graph, I feel that the white region should be the solution of the vectors and region is two dimensional and not a single line.
That was my first question,
I read some answers on the internet that said that the set of all vectors orthogonal to a non zero vector lie on a single line passing through the origin. Why does the line have to pass through the origin and what does passing through the origin mean if a vector is a free vector.