Question

Which of the following vectors are orthogonal to (-1,3)?

Answer 1

Any vector that is a multiple of (3, 1) will be orthogonal. These include
.. A (-6, -2)
.. D (3, 1)

_____
The dot-product of these with (-1, 3) is zero:
(-6*-1 +-2*3) = 6 -6 = 0
(3*-1 +1*3) = -3 +3 = 0

You can make a vector orthogonal to a 2-D vector by swapping the coordinates and negating one of them. When you swap the elements of (-1, 3) you get (3, -1). It is usually convenient to negate the one that is already negative, so that would give you (3, 1) as the orthogonal vector.