Jawaban:

A) B ( 5, 8, 3)

B) 3 : -1

Penjelasan dengan langkah-langkah:

rumus kolinier:

→ 3 titik berada dalam satu garis

⃗⃗⃗⃗AB = k . AC

dimana

AB = ⃗b - ⃗a

AC = ⃗c - ⃗a

Diketahui:

⃗a= (2, 5,0)

⃗b = (x, y, 3)

⃗c = (4, 7, 2)

Ditanya:

A. koordinat B

B. perbandingan AB : BC

JAWAB:

AB = ⃗b - ⃗a =(x, y, 3) -(2, 5,0)

= ( x-2, y-5, 3)

AC = ⃗c - ⃗a = (4, 7, 2) - ( 2, 5,0)

= ( 4-2 , 7-5 , 2-0) = (2, 2, 2)

AB = k . AC

( x-2, y-5, 3) = k. (2, 2, 2) = (2k,2k,2k)

Jadi :

x-2 = 2k

y-5 = 2k

3 = 2k → k = 3/2

x-2 = 2k

x-2 = 2. 3/2

x = 5

y-5 = 2k

y-5 = 2. 3/2

y = 8

B ( 5, 8, 3)

AB : BC = ( ⃗b - ⃗a) : ( ⃗c - ⃗b)

= ( 5, 8, 3) - (2, 5,0) : (4, 7, 2)- ( 5, 8, 3)

= (3, 3,3) : (-1, -1,-1)

= 3 : -1 → tanda negatif

jadi titik C diantara A dan B

urutan titiknya : A, C, B