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109學測數學考科-03


<單選題>

如圖所示,\(O\)為正六邊形之中心。試問下列哪個向量的終點P落在\(\triangle ODE\)內部(不含邊界)?
(1) \(\overset{\rightharpoonup}{OP} = \overset{\rightharpoonup}{OC} + \overset{\rightharpoonup}{OE}\)
(2) \(\overset{\rightharpoonup}{OP} = \frac{1}{4} \overset{\rightharpoonup}{OC} + \frac{1}{2} \overset{\rightharpoonup}{OE}\)
(3) \(\overset{\rightharpoonup}{OP} = -\frac{1}{4} \overset{\rightharpoonup}{OC} + \frac{1}{2} \overset{\rightharpoonup}{OE}\)
(4) \(\overset{\rightharpoonup}{OP} = \frac{1}{4} \overset{\rightharpoonup}{OC} – \frac{1}{2} \overset{\rightharpoonup}{OE}\)
(5) \(\overset{\rightharpoonup}{OP} = -\frac{1}{4} \overset{\rightharpoonup}{OC} – \frac{1}{2} \overset{\rightharpoonup}{OE}\)。

答案

令 \(\overset{\rightharpoonup}{OP} = x \overset{\rightharpoonup}{OC} + y \overset{\rightharpoonup}{OE}\),P落在直線OE右側的條件為 \(x \gt 0\),落在直線OD左側的條件為 \(x - y \lt 0\),落在直線DE下方的條件為 \(y \lt 1\),故選(2)。 報錯
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