Question

Fie vectorii u si v cu |u|=2 si |v|=3 si u•v=-5 (cu vector). Calculati |u+v| si |u-v| (cu vectori)

Answer 1

|u| = 2 => √(u²) = 2 => u² = 4
|v| = 3 => √(v²) = 3 => v² = 9
u•v = -5

|u+v| = √[(u+v)²] = √(u²+2•u•v+v²) =
= √(4+2•(-5)+9) = √(13-10) = √3

|u-v| = √[(u-v)²] = √(u²-2•u•v+v²) =
= √(4-2•(-5) +9) = √(13+10) = √(23)