What is an orthogonal vector to (4, 2)?

Answer 1

Let (x,y) be such a vector then (x,y).(4,2)=0

4x+2y=0

y=-2x

(x,y)=(x,-2x)=x(1,-2)

So all such vectors are orthogonal to (4,2)

We can set x=1 to get one such vector to be

(1,-2)