Matematika tolong bantu di jawab! memakai cara !!​

krystelmetzulv – June 01, 2023

tolong bantu di jawab! memakai cara !!​

Jawab:

vektor

perkalian  titik

sudut vektor

u =  1, √2, a

|u| = √(1² + (√2)² +  (a)²)
|u| = √ (1+ 2+ a²)
|u| =  √(3 + a²)

v =  1 ,- √2, a

|v|= (1² + (-√2)² +  (a)²)
|v| = √ (1+ 2+ a²)
|v| =  √(3 + a²)

|u|.|v| =  3+ a²

u.v = 1(1) + √2(-√2) + a(a)
u.v = 1 -2 +a²
u.v = - 1 + a²

[tex]\sf cos (u ,v) = \dfrac{u.v}{|u|. |v|}[/tex]

[tex]\sf cos (\frac{\pi}{3}) = \dfrac{-1+ a^2}{3+a^2}[/tex]

[tex]\sf\dfrac{1}{2}= \dfrac{-1+a^2}{3+a^2}[/tex]

2(-1 + a²)=  1 (3 + a²)
-2 + 2a² =  3 + a²
2a² - a² =  3 + 2
a² =  5
a =  ±√5