已知向量
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,則
(Ⅰ)與
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同向的單位向量的坐標(biāo)表示為____________;
(Ⅱ)向量
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與向量
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夾角的余弦值為____________。
(Ⅰ)
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;(Ⅱ)
(Ⅰ)由
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,得
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.設(shè)與
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同向的單位向量為
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,則
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且
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,解得
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故
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.即與
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同向的單位向量的坐標(biāo)為
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.
(Ⅱ)由
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,得
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.設(shè)向量
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與向量
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的夾角為
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,則
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.
【點(diǎn)評】本題考查單位向量的概念,平面向量的坐標(biāo)運(yùn)算,向量的數(shù)量積等.與某向量同向的單位向量一般只有1個(gè),但與某向量共線的單位向量一般有2個(gè),它包含同向與反向兩種.不要把兩個(gè)概念弄混淆了. 來年需注意平面向量基本定理,基本概念以及創(chuàng)新性問題的考查
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
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(
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,
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與
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四個(gè)
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分別滿足下列條件,
(1)
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
;
(3)
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,
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