Question

Find the angle between the vectors u and v. Express your answer in degrees

and round to the nearest tenth of a degree.
u = {5,-5,-9), v=(-8,1,-2)

Answer 1

The angle between the vectors u and v is found using the dot product and the magnitudes of the vectors, followed by computing the arccosine of the resulting value to obtain the angle in degrees.

Step-by-step explanation:

The angle between two vectors u and v can be found using the dot product formula, which is defined by u · v = |u| |v| cos(θ), where θ is the angle between the vectors and |u| and |v| are the magnitudes of vectors u and v, respectively. For vectors u = {5, -5, -9} and v = {-8, 1, -2}, we first compute the dot product of u and v, which is (5)(-8) + (-5)(1) + (-9)(-2). After finding the magnitudes of both vectors, we then use the dot product and magnitudes to calculate cos(θ) and, subsequently, the angle θ in degrees using the arccosine function.