（英文）題Find the position vector of a point R which divides the

題目：

（英文）題
Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are i + 2j - k and -i + j - k respectively in the ratio 2:1 internally and externally
還有知道A(3,2,-1),B(2,3,4) 和 C(0,5,14) 三個點,怎麼證明它們在同一條直線上?

解答：

1.
若R在PQ間
R(1/3,4/3,-1)
若R在PQ外
R（-3,-2,-1）
2.
OA=(3,2,-1),OB=(2,3,4),OC=(0,5,14)
OC=λOA+（1-λ)OB
(0,5,14)=λ(3,2,-1)+(1-λ)(2,3,4)
λ=-2