Diketahui segitiga pqr dg pq=(2,3,4),pr=(3,2,1) dan a membagi pr dg 1:2 , b membagi qr dg 2:1 maka panjang ab? Mbak/mas/kaka tolong ya

A membagi PR = 1 : 2
=> PA : AR = 1 : 2 => PA/AR = 1/2 => AR = 2 PA

PR = (3, 2, 1)
PA + AR = (3, 2, 1)
PA + 2 PA = (3, 2, 1)
3PA = (3, 2, 1)
PA = (1, 2/3, 1/3)
a - p = (1, 2/3, 1/3)
a = p + (1, 2/3, 1/3)

B membagi QR = 2 : 1
=> QB : BR = 2 : 1 => QB/BR = 2/1 => QB = 2 BR

QR = QR
QB + BR = QP + PR
2 BR + BR = -PQ + PR
3 BR = (-2, -3, -4) + (3, 2, 1)
3 BR = (1, -1, -3)
BR = (1/3, -1/3, -1)
r - b = (1/3, -1/3, -1)
b = r - (1/3, -1/3, -1)

AB = b - a
= r - (1/3, -1/3, -1) - (p + (1, 2/3, 1/3))
= r - p - (1/3, -1/3, -1) - (1, 2/3, 1/3)
= (r - p) - ((1/3, -1/3, -1) + (1, 2/3, 1/3))
= PR - (4/3, 1/3, -2/3)
= (3, 2, 1) - (4/3, 1/3, -2/3)
= (5/3, 5/3, 5/3)

Panjang AB = |AB| = √((5/3)^2 + (5/3)^2 + (5/3)^2)
= √(25/9 + 25/9 + 25/9)
= √(75/27)
= √(25/9)
= 5/3