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A,B,C are vertices of a triangle ABC hav...

A,B,C are vertices of a `triangle ABC` having posiiton vectors `3 hat i-hat j+2hat k`,`5 hat i+2 hat j+ 4 hat k`and `-hat i-hat j+6 hatk` respectively. D is a point on BC such that `(BD)/(DC)=2/1` and E is the midpoint of AC. If AD and BE intersect at a point P then PB:PE is equal to

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