diketahui koordinat titik p(5,4,-1) dan q (2,-2,5) jika pa : aq = 2 : 1 koordinat titik a adalah

jawab

PA : AQ  = 2 : 1
PA = 2 AQ
a-p = 2(q-a)
a  - p = 2q - 2a
a + 2a = p + 2q
3a = p + 2q
a = 1/3 { p + 2q }

ax = 1/3 (px + 2qx) = 1/3 (5 + 2(2)) = 1/3(9)= 3
ay = 1/3 (py + 2qy) = 1/3 (4 + 4(-2)) = 1/3 (-4) = - 4/3
az = 1/3 (pz + 2qz ) = 1/3 (-1 + 2(5)) = 1/3(9) = 3

A(ax,ay,az) = (3, - 4/3, 3)