Final answer:
The angle between two vectors is calculated using the dot product, which involves dividing the dot product of the vectors by the product of their magnitudes and then taking the inverse cosine of that quotient.
Step-by-step explanation:
In mathematics, particularly in vector analysis, the angle between two vectors can be found using the dot product. For vectors A and B, this is calculated by dividing the dot product of A and B by the product of the magnitudes of the two vectors and taking the inverse cosine of the result. The dot product formula is given by A · B = AxBx + AyBy + AzBz. The challenge problem presented asks to find the angle between two vectors with magnitudes of 5.0 cm and 4.0 cm and resultant vectors of 3.0 cm when added and subtracted. This can be solved using vector addition and subtraction rules, trigonometry, and the cosine law for vectors.