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Finding vector problem
m= 1

Solution: Make diameter BD, connecting DA and DC, so there is.

Vector OB=- vector OD

It is easy to know that H is the favorite of △ABC.

∴CH⊥AB,AH⊥BC

∫BD is diameter

∴DA⊥AB,DC⊥BC

∴CH//AD,AH//CD

So the quadrilateral AHCD is a parallelogram.

∴ vector AH= vector DC

Vector DC= vector OC- vector OD= vector OC+ vector OB

So, I have to

Vector OH= vector OA+ vector AH= vector OA+ vector DC= vector OA+ vector OB+ vector OC

Comparing the coefficients, we get m= 1.