Question

已知向量OA,OB,OC.在三角形ABC的中线AM上任取一点P,试用向量OA,OB,OC表示向量AP.高中必修四.

Answer 1

P is on AM

let

|AP|/|PM|=k

OP = (OA+kOM)/(1+k)

= (OA + k(OB+OC)/2)/(1+k) ( M is mid point BC)

= (2OA+k(OB+OC))/(2(1+k))

OA+AP = (2OA+k(OB+OC))/(2(1+k))

AP = k(-2OA+OB+OC)/(2(1+k))