Perpendicular vector from $(\cos(\theta)x, \sin(\theta)x)$

Question

Hi want to know how to compute a perpendicular vector from a vector that contains non-integer-- for example if my vector is like $(cos(\theta)x, sin(\theta)x)$, is it possible to compute one vector that is perpendicular to it?

Answer 1

In 2 dimensions, $(a,b)$ and $(-b, a)$ (or $(b, -a)$) are perpendicular. You can check it with the dot product: $$(a, b) \cdot (-b, a)=a*(-b)+b*a=-ab+ba=0$$