Find the angle between two vectors. In radians and in degrees.

u=<1,0,-3>, v=<2,-2,1>

I got

radians = 1.676

degrees = 96

u•v = |u|*|v|*cosθ

-1 = √10*√5 cosθ
θ = 81.9°

check your math (and mine!)

To find the angle between two vectors, we can use the dot product formula:

𝐮 · 𝐯 = |𝐮| |𝐯| cos(θ)

Where 𝐮 and 𝐯 are the given vectors, |𝐮| and |𝐯| are the magnitudes of the vectors, and θ is the angle between them.

First, let's find the magnitudes of the given vectors:
|𝐮| = √(1^2 + 0^2 + (-3)^2) = √(1 + 0 + 9) = √10
|𝐯| = √(2^2 + (-2)^2 + 1^2) = √(4 + 4 + 1) = √9 = 3

Next, we can calculate the dot product of the two vectors:
𝐮 · 𝐯 = (1)(2) + (0)(-2) + (-3)(1) = 2 + 0 - 3 = -1

Now, let's substitute the known values into the equation and solve for θ:
-1 = √10 * 3 * cos(θ)
cos(θ) = -1 / (3√10)

To find the angle in radians, we can use the inverse cosine (arccos) function:
θ = arccos(-1 / (3√10)) ≈ 1.676 radians

To convert the angle from radians to degrees, we can use the conversion factor:
1 radian ≈ 57.3 degrees

θ_degrees = 1.676 * 57.3 ≈ 96 degrees

So, the angle between the vectors is approximately 1.676 radians or 96 degrees.