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Let O A C B be a parallelogram with O at...

Let `O A C B` be a parallelogram with `O` at the origin and`O C` a diagonal. Let `D` be the midpoint of `O Adot` using vector methods prove that `B Da n dC O` intersect in the same ratio. Determine this ratio.

Text Solution

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The correct Answer is:
`2:1`
Let OACB be a parallelogram shown as

Here, `OD=(1)/(2)BC`
`implies Opi+PD=(1)/(2)(BP+PC)` [using `Delta` law]
`implies 2OP+2PD=BP+PC`
`implies -2PO+2PD=-PB+PC`
`implies PB+2PD=PC+2PO`
`implies (PB+2PD)/(1+2)=(PC+2PO)/(1+2)`
the common point P of BD and CO divides each in the ratio 2:1.
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