Finding the angle between two lines
Given lines: $$l_1 = [3, 1, -1] + t[2, -2, 3]$$ $$l_2 = [5, -1, 2] + t[1, -3, 5]$$
I tried cross product equation of finding the angle: $\cos^{-1}(\sqrt{426} / (\sqrt{17} \times \sqrt{35})) = 57.8$ degree
Then I tried dot product equation of finding the angle: $\sin^{-1}(23 / (\sqrt{17} \times \sqrt{35})) = 19.5$ degree
The correct answer is the latter dot product equation, but I don't understand why the cross product equation failed me in this instance.
Can someone clarify this for me? Thanks.