When given any two vectors, it is possible to use the dot product to find the angle between the vectors without having any ambiguity as it uses the inverse cosine function. However, when we use the cross product the inverse sine function can cause ambiguity. In other scenarios it is possible to detect the ambiguous case so I was wondering if it is possible in the scenario of two vectors? If so, how?
2026-03-28 10:14:54.1774692894
Finding the Angle Between Two Vectors Using Cosine Law
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One way would be to also compute the dot product. If that is positive, then the angle is between -90° and 90°, if it is negative, it is outside.
In other words, if the "inverse cosine" you are referring to could be both 30° and 150°, check what the dot product gives you. If it's a positive number, then the true answer is 30°, otherwise it's 150°.