bantuin dong kak!! pentinggg : )

AR : RB = m : n => r = (mb + na)/(m + n)

AR : RB = 3 : 1
r = (3b + 1a)/(3 + 1)
r = [(6, -12, 9) + (6, 4, 7)]/4 = (12, -8, 16)/4 = (3, -2, 4)
PR = r - p = (3, -2, 4) - (-1, 4, 2) = (4, -6, 2)
|PR| = √(4^2 + (-6)^2 + 2^2) = √(16 + 36 + 4) = √56 = 2√14

Semoga membantu:)

Vektor

1.A(2,1),, B(-2,-3), C(-4,5)
P tengah AB  --> AP = PB
p - a = b - p  --> 2p = a +b
P = 1/2 (a+b)
P = 1/2 { (-2,-3)+(2,1)} = 1/2 (0,-2)
P = (0, -1)

Q tengah BC --> Q = 1/2 (b+c)
Q=1/2 {(-2,3)+(-4,5)} = 1/2 (-6, 8)
Q= (-3, 4)

R tengah AC
R = 1/2 (a+c) = 1/2 {(-2), (6)}
R = (-1, 3)

(3) A(1,4,6), B(1,0,2), C(2,-1,5)
AP :PB = 3 : 1
AP = 3 PB --> p-a = 3(b-p) --> p - a = 3b - 3p
p+ 3p = 3b + a
4p = 3b + a
p = 1/4 { 3(b) + (a)}
p = 1/4 { (3,0,6) +(1,4,6)} = 1/4 {(4, 4, 12)
P = (1, 1, 3)

PC = c -  p = {(2, -1, 5) - (1, 1, 3)}
PC = (2-1), (-1-1), (5-3)
PC= (1, -2, 2)
|PC| = | √((1)² +(-2)² +(2)²)| = |√9|
PC  = 3