Find a vector that is perpendicular to.

The rule is that is perpendicular to. You swap the coordinates and then change the sign of one of the coordinates.

In this case, a = - 6 and b = 4

=

=

Compute the dot product of the two vectors

dot = (-6) (4) + (4) (6) = - 24 + 24 = 0

Since the dot product is 0, this confirms that is perpendicular to the given vector.

note: any scale factor of will work as well. For example, is another possible answer since you multiply both parts of the answer above by the value 2. So there are infinitely many answers in the form where k is any real number.