Vectors Problem - Find the angles between u=(7,2,-5) and v=(9,-1,-6). Please include steps.

Question

There are small arrows on top of u and v that point right (format won't let me add)

Answer 1

Hi Amanda,

Try using the dot product formula

u (dot) v = ||u||*||v||* cos(θ)

u (dot) v = u₁v₁ + u₂v₂ + u₃v₃

||u|| = √[(u₁)² + (u₂)² + (u₃)²]

θ is the angle between the vectors

Answer 2

To tackle this problem, you will be using one theorem: the DOT product of two vectors equals to the product of their magnitudes and the cosine of their angle.

DOT(u,v) = |u| * |v| * Cos(θ)

I won't provide numbers here, but include essential steps for you to move forward:

1. Calculate the magnitude of vector u and v: |u|, |v|, which you should know how or Google.
2. Calculate the dot product of u and v: DOT(u,v) = u₁*v₁ + u₂*v₂ + u₃*v₃, where u₁ etc. are the components of the vectors, eg. u₁=7
3. Calculate Cos(θ), and then θ using your calculator.