已知a1={1,2,-3},a2={2,-3,x},a3={-2,x,6}. (Ⅰ)如a1⊥a2,则x=_____________; (Ⅱ)如a1∥a3,则x=_____________; (Ⅲ)如a1,a2,a3共面,则x=_____________.

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问题 已知a1={1,2,-3},a2={2,-3,x},a3={-2,x,6}.
(Ⅰ)如a1⊥a2,则x=_____________;
(Ⅱ)如a1∥a3,则x=_____________;
(Ⅲ)如a1,a2,a3共面,则x=_____________.

选项

答案(Ⅰ)[*] (Ⅱ)-4 (Ⅲ)-4或-6

解析 (Ⅰ)a1⊥a2a1.a2=0,故1.2+2.(-3)+(-3)x=0,得x=
(Ⅱ)a1∥a3,得x=-4.
(Ⅲ)a1,a2,a3共面(a1,a2,a3)=0,故=0,得x=-4或-6.
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