C
分析:因?yàn)橄蛄?img class='latex' src='http://thumb.zyjl.cn/pic5/latex/226087.png' />成為空間一組基底時(shí),所以,這三個(gè)向量不共面,看各個(gè)選項(xiàng)中的條件哪個(gè)能使
向量
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不共面.
解答:因?yàn)橄蛄?img class='latex' src='http://thumb.zyjl.cn/pic5/latex/226087.png' />成為空間一組基底時(shí),所以,這三個(gè)向量不共面,
若A、B、C互不重合且無三點(diǎn)共線,點(diǎn)M與A、B、C共面的條件是
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=x
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+y
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+z
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,且x、y、z為實(shí)數(shù).
A 不滿足條件,因?yàn)橛墒阶涌傻肕、A、B、C共面,故這三個(gè)向量共面.
由B可得
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-
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≠
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-
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+
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-
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,即
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≠
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+
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-
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,
但仍有可能使 M、A、B、C共面,故B不滿足條件.
D中的向量
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在同一個(gè)平面內(nèi),故不滿足條件.
通過排除,只有選 C.
故選C
點(diǎn)評:本題考查空間向量基本定理及其意義,以及三個(gè)向量共面的條件和性質(zhì).