【答案】
分析:(1)當(dāng)
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時(shí),求出向量
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、
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,利用數(shù)量積的坐標(biāo)運(yùn)算求出向量
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•
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,從而求出向量
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、
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的夾角θ;(2)向量
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,
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,代入函數(shù)
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,利用三角函數(shù)的誘導(dǎo)公式進(jìn)行化簡(jiǎn),轉(zhuǎn)化為三角函數(shù)在定區(qū)間上的最值,即可求得結(jié)果.
解答:解:(1)當(dāng)
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時(shí),
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,
所以
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,
因而
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;
(2)
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,
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,
因?yàn)?img src="http://thumb.zyjl.cn/pic6/res/gzsx/web/STSource/20131024182121870196930/SYS201310241821218701969019_DA/16.png">,
所以
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,
當(dāng)λ>0時(shí),
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,即
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,
當(dāng)λ<0時(shí),
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,即
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,
所以
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.
點(diǎn)評(píng):此題是個(gè)中檔題.考查向量的數(shù)量積的坐標(biāo)運(yùn)算以及向量的夾角,和三角函數(shù)的誘導(dǎo)公式和三角函數(shù)在定區(qū)間上的最值等基礎(chǔ)知識(shí),同時(shí)也考查了學(xué)生靈活應(yīng)用知識(shí)分析解決問題的能力.