tiwaiii95
Kelas : X Mata Pelajaran : Matematika Peminatan Bab : Vektor
31. a.vektor d d = 2a + b - c d = 2(2, 3, -1) + (-2, -1, 2) - (3, 4, 5) d = (4, 6, -2) + (-2, -1, 2) - (3, 4, 5) d = (-1, 1, -5) b. panjang vektor d ΙdΙ = √(-1)² + 1² + (-5)² ΙdΙ = √27 ΙdΙ = 3√3 32. a. koordinat titik P Pembagian dalam bentuk vektor : Titik P = mB + nA / m+n Titik P = 3(2, 6, 9) + (-2, 6, 5) / 4 Titik P = (6, 18, 27) + (-2, 6, 5) / 4 Titik P = (4, 24, 32) / 4 Titik P = (1, 6, 8) b. vektor yg diwakili oleh PC PC = C - P PC = (5, 5, 7) - (1, 6, 8) PC = (4, -1, -1)
33. I a+b I² = 37 37 = IaI² + IbI² + 2ab 37 = IaI² + IbI² + 12 25 = IaI² + IbI² I a-b I² = IaI² + IbI² - 2ab I a-b I² = 25 - 12 I a-b I² = 13 I a-b I = √13
34. a. vektor AB dan vektor AC AB = B-A AB = (4, 1, 3) - (2, -1, 4) AB = (2, 2, -1) AC = C-A AC = (2, 0, 5) - (2, -1, 4) AC = (0, 1, 1) b. cos α AB dan AC cos α = a×b / IaI×IbI IaI = √2² + 2² + (-1)² IaI = 3 IbI = √0² + 1² + 1² IbI = √2 cos α = a×b / IaI×IbI cos α = 2×0 + 2×1 + (-1)×1 / 3√2 cos α = 1/3√2
35. a. vektor c IbI = √2² + (-6)² + 4² IbI = √56 c = a×b/IbI² × b c = 4×2 + (-2)×(-6) + 2×4 / (√56)² × (2, -6, 4) c = 28/56 × (2, -6, 4) c = 1/2 × (2, -6, 4) c = (1, -3, 2) b. panjang vektor c IcI = √1² + (-3)² + 2² IcI = √14
Mata Pelajaran : Matematika Peminatan
Bab : Vektor
31.
a. vektor d
d = 2a + b - c
d = 2(2, 3, -1) + (-2, -1, 2) - (3, 4, 5)
d = (4, 6, -2) + (-2, -1, 2) - (3, 4, 5)
d = (-1, 1, -5)
b. panjang vektor d
ΙdΙ = √(-1)² + 1² + (-5)²
ΙdΙ = √27
ΙdΙ = 3√3
32.
a. koordinat titik P
Pembagian dalam bentuk vektor :
Titik P = mB + nA / m+n
Titik P = 3(2, 6, 9) + (-2, 6, 5) / 4
Titik P = (6, 18, 27) + (-2, 6, 5) / 4
Titik P = (4, 24, 32) / 4
Titik P = (1, 6, 8)
b. vektor yg diwakili oleh PC
PC = C - P
PC = (5, 5, 7) - (1, 6, 8)
PC = (4, -1, -1)
33.
I a+b I² = 37
37 = IaI² + IbI² + 2ab
37 = IaI² + IbI² + 12
25 = IaI² + IbI²
I a-b I² = IaI² + IbI² - 2ab
I a-b I² = 25 - 12
I a-b I² = 13
I a-b I = √13
34.
a. vektor AB dan vektor AC
AB = B-A
AB = (4, 1, 3) - (2, -1, 4)
AB = (2, 2, -1)
AC = C-A
AC = (2, 0, 5) - (2, -1, 4)
AC = (0, 1, 1)
b. cos α AB dan AC
cos α = a×b / IaI×IbI
IaI = √2² + 2² + (-1)²
IaI = 3
IbI = √0² + 1² + 1²
IbI = √2
cos α = a×b / IaI×IbI
cos α = 2×0 + 2×1 + (-1)×1 / 3√2
cos α = 1/3√2
35.
a. vektor c
IbI = √2² + (-6)² + 4²
IbI = √56
c = a×b/IbI² × b
c = 4×2 + (-2)×(-6) + 2×4 / (√56)² × (2, -6, 4)
c = 28/56 × (2, -6, 4)
c = 1/2 × (2, -6, 4)
c = (1, -3, 2)
b. panjang vektor c
IcI = √1² + (-3)² + 2²
IcI = √14