Bantuannya .... #No_Spam Materi : Vektor kelas : ⑩ Sma

1) (a + b)(a + b) = 16
a.a + 2a.b + b.b = 16
|a|^2 + 2a.b + |b|^2 = 16
6^2 + 2.a.b + 4^2 = 16
36 + 2.a.b + 16 = 16
2a.b = -36
a.b = -18

2) |a - b|^2 = a.a - 2a.b + b.b
= |a|^2 - 2|a|.|b| cos 60° + |b|^2
= 4^2 - 2 . 4 . 5 . 1/2 + 5^2
= 16 - 20 + 25
= 21
|a - b|^2 = 21
|a - b| = √21

3) A(4, -1, 2), B(5, 2, 5), C(-3, 4, 0)
AB = b - a = (5, 2, 5) - (4, -1, 2) = (1, 3, 3)
BC = c - b = (-3, 4, 0) - (5, 2, 5) = (-8, 2, -5)
AC = c - a = (-3, 4, 0) - (4, -1, 2) = (-7, 5, -2)

a)AB.BC = (1, 3, 3).(-8, 2, -5) = 1(-8) + 3(2) + 3(-5) = -8 + 6 - 15 = -17

b)AB.AC = (1, 3, 3).(-7, 5, -2) = 1(-7) + 3(5) + 3(-2) = -7 + 15 - 6 = 2

4) P(2, 2x, 0), Q(-1, 1, -7), R(3x, 3, x)
PQ = q - p = (-1, 1, -7) - (2, 2x, 0) = (-3, 1 - 2x, -7)
PR = r - p = (3x, 3, x) - (2, 2x, 0) = (3x - 2, 3 - 2x, x)
PQ.PR = -23
(-3, 1 - 2x, -7).(3x - 2, 3 - 2x, x) = -23
-3(3x - 2) + (1 - 2x)(3 - 2x) + -7x = -23
-9x + 6 + 3 - 2x - 6x + 4x^2 - 7x + 23 = 0
4x^2 - 24x + 32 = 0
x^2 - 6x + 8 = 0
(x - 4)(x - 2) = 0
x = 4 atau x = 2