Question

Find the angle between the given vectors to the nearest tenth of a degree.

a) sin⁻¹(magnitude(u)×magnitude(v))
b) cos⁻¹(u⋅v/magnitude(u)×magnitude(v))
c) tan⁻¹(u×v/u⋅v)
d) sec⁻¹(magnitude(u)/(magnitude(v))

Answer 1

To find the angle between two vectors, use the inverse cosine of the dot product of vectors divided by the product of their magnitudes, then convert it to degrees if needed.

Step-by-step explanation:

The question deals with finding the angle between two vectors. The correct expression to use for this purpose is option b) cos⁻¹(u⋅v/magnitude(u)×magnitude(v)). This formula is derived from the dot product of vectors, also known as the scalar product, which provides the cosine of the angle when divided by the product of the vectors' magnitudes. To find the angle between two vectors, A and B, you can calculate the dot product (A⋅B), then divide by the product of the magnitudes of vectors A and B and finally take the inverse cosine of the result (cos⁻¹). This process will give you the angle in radians, which can then be converted into degrees if necessary.