How to calculate vector normal to an eigen vector?

Can anyone please tell me how to calculate vector normal to an eigen vector? I was also asked to calculate the size of the two lines that are delimited between the origin and the further data point situated nearest the line. Can anyone please help me in solving this step? Thank you

[Roger Stafford]

First, there is nothing unique about a vector being normal to another vector unless you are in two-dimensional space. Is this in 2D?

Second, I think you can do much better at stating the question in the second sentence. What "lines" are you talking about and what do you mean by "delimiting" those lines? Please try to explain this in much greater detail. You are much more likely to receive a satisfactory answer if you do. Perhaps you can give a concrete example. Otherwise the best you can hope for are wild guesses.

[Shivakumar]

I have a two dimensional data. By using Principal Component Analysis, I got eigen vectors A=[-0.8622 0.5655;0.5065 0.8622]. Now I was asked to plot the eigen vector and to obtain its perpendicular line.