(英文)题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还有知道A(3,2,-1),B(2,3,4) 和 C(0,

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(英文)题FindthepositionvectorofapointRwhichdividesthelinejoiningtwopointsPandQwhosepositionvectorsarei+

(英文)题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还有知道A(3,2,-1),B(2,3,4) 和 C(0,
(英文)题
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
还有知道A(3,2,-1),B(2,3,4) 和 C(0,5,14) 三个点,怎么证明它们在同一条直线上?

(英文)题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还有知道A(3,2,-1),B(2,3,4) 和 C(0,
1.
若R在PQ间
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

找到一个点R的划分界限为连接两点P和Q的位置向量位置向量是我+ 2j - k和- i十j - 钾分别在2:1的比例从内部和外部

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