Assume that 𝑢⋅𝑣=3, ‖𝑢‖=8, and ‖𝑣‖=4. What is the value of 8𝑢⋅(𝑢−9𝑣)?

Question

Assume that 𝑢⋅𝑣=3, ‖𝑢‖=8, and ‖𝑣‖=4. What is the value of 8𝑢⋅(𝑢−9𝑣)?

Answer 1

8u • (u - 9v) = 8u • u - 72 u • v

As ||u|| = 8, u • u = 64

Then, 8u • u - 72 u • v = 8 * 64 - 72 * 3 =512 - 216 = 296