If L, M, N are the midpoints of the sides PQ, | vedclass

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(C) In $	riangle PQR$,$L, M, N$ are midpoints of $PQ, QR, RP$ respectively.By the midpoint theorem,$\overrightarrow{LM} = \frac{1}{2} \overrightarrow

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$\vec{0}$

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(C) In $	riangle PQR$,$L, M, N$ are midpoints of $PQ, QR, RP$ respectively.By the midpoint theorem,$\overrightarrow{LM} = \frac{1}{2} \overrightarrow{PR}$,$\overrightarrow{MN} = \frac{1}{2} \overrightarrow{PQ}$,and $\overrightarrow{NL} = \frac{1}{2} \overrightarrow{QR}$.Also,$\overrightarrow{QM} = \frac{1}{2} \overrightarrow{QR} = \overrightarrow{NL}$,$\overrightarrow{LN} = \frac{1}{2} \overrightarrow{PR} = \overrightarrow{ML}$,$\overrightarrow{RN} = \frac{1}{2} \overrightarrow{RP} = -\frac{1}{2} \overrightarrow{PR} = -\overrightarrow{ML}$.Substituting these into the expression:$\overrightarrow{QM} + \overrightarrow{LN} + \overrightarrow{ML} + \overrightarrow{RN} - \overrightarrow{MN} - \overrightarrow{QL}$$= \overrightarrow{NL} + \overrightarrow{ML} + \overrightarrow{ML} - \overrightarrow{ML} - \overrightarrow{MN} - \overrightarrow{QL}$Since $\overrightarrow{QL} = -\overrightarrow{LQ} = -\overrightarrow{MN}$,the expression simplifies to $\vec{0}$.

If $L, M, N$ are the midpoints of the sides $PQ, QR$ and $RP$ of $\triangle PQR$ respectively,then $\overrightarrow{QM} + \overrightarrow{LN} + \overrightarrow{ML} + \overrightarrow{RN} - \overrightarrow{MN} - \overrightarrow{QL} = $

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