PQRS is a parallelogram. If \vec{PR}=\vec{a} and \vec{QS}=\vec{b}, then what is \vec{PQ} equal to?
- A. \vec{a}+\vec{b}
- B. \vec{a}-\vec{b}
- C. \frac{\vec{a}+\vec{b}}{2}
- D. \frac{\vec{a}-\vec{b}}{2} ✓
Correct Answer: D. \frac{\vec{a}-\vec{b}}{2}
Explanation
By triangle law in \Delta PQR and \Delta PQS, we have \vec{PQ} + \vec{QR} = \vec{PR} = \vec{a}. Since PQRS is a parallelogram, \vec{QR} = \vec{PS}. Also, \vec{PQ} - \vec{PS} = \vec{SQ} = -\vec{QS} = -\vec{b}. Adding the two equations \vec{PQ} + \vec{PS} = \vec{a} and \vec{PQ} - \vec{PS} = -\vec{b} yields 2\vec{PQ} = \vec{a} - \vec{b}, or \vec{PQ} = \frac{\vec{a}-\vec{b}}{2}.
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