Tolong dibantu nomer 8,10 dan 11 nya

11) a = 3i + 4j + 5k
=> |a| = √(3^2 + 4^2 + 5^2) = √(9 + 16 + 25) = √50 = 5√2
b = -2i + 8j + 2k
=> |b| = √((-2)^2 + 8^2 + 2^2) = √(4 + 64 + 4) = √72 = 6√2
Cos @ = a.b / |a|.|b|
Cos @ = (3(-2) + 4(8) + 5(2)) / (5√2)(6√2)
Cos @ = (-6 + 32 + 10) / 60
Cos @ = 36/60 = 6/10 = 3/5 = sa/mi
de = √(5^2 - 3^2) = √(25 - 9) = √16 = 4
Sin @ = de/mi = 4/5
Sin 2@ = 2 sin @ cos @ = 2 . 4/5 . 3/5 = 24/25

10) ABCD jajar genjang maka AB = DC
=> b - a = c - d
=> d = a + c - b = (6,4,2) + (2,2,-2) - (-1,3,7) = (9,3,-7)
@ = sudut antara AC dan BD
AC = c - a = (2,2,-2) - (6,4,2) = (-4,-2-4)
=> |AC| = √((-4)^2 + (-2)^2 + (-4)^2) = √(16 + 4 + 16) = √36 = 6
BD = d - b = (9,3,-7) - (-1,3,7) = (10, 0, -14)
=> |BD| = √(10^2 + 0^2 + (-14)^2) = √(100 + 0 + 196) = √296 = 2√74
Cos @ = AC.BD / |AC|.|BD|
= (-4(10) + (-2)(0) + (-4)(-14)) / 6 . 2√74
= (-40 + 0 + 56) / 12√74
= 4 / 12√74
= 1 / 3√74