Science:Math Exam Resources/Courses/MATH152/April 2022/Question A18/Hint 2

Here is a hack that allows for a quick solution just in this case. The question statement already tells us that the composite ${\mathit {Ref}}_{50^{\circ }}\circ {\mathit {Ref}}_{30^{\circ }}$ is a rotation, so we just need to compute what it does to a single vector, for example a unit vector that is fixed by ${\mathit {Ref}}_{30^{\circ }}$.