𝑢 and 𝑣 are two vectors such that ‖𝑢+𝑣‖=5 and ‖𝑢−𝑣‖=1. Find 𝑢⋅𝑣.

Answer 1

||u + v||² =(u + v)² = |u|²+ 2u•v + |v|² = 25

||u - v||² =(u - v)² = |u|²- 2u•v + |v|² = 1

Sabtracting, we get: 4u•v = 24 and u•v = 6