个向量之和为零向量;
④不相等的两个空间向量的模必不相等.
其中,真命题的序号为________.
① [①真命题,向量\s\up8(→(→)与\s\up8(→(→)是相反向量,长度相等;②假命题,终点应构成一个球面;③假命题,当它们首尾顺次相接时,其和才为零向量;④假命题,不相等的两个向量的模可以相等.]
7.化简\s\up8(→(→)-\s\up8(→(→)+\s\up8(→(→)-\s\up8(→(→)-\s\up8(→(→)=________.
【导学号:33242239】
\s\up8(→(→) [\s\up8(→(→)-\s\up8(→(→)+\s\up8(→(→)-\s\up8(→(→)-\s\up8(→(→)=\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)=\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)=\s\up8(→(→).]
8.化简:(\s\up8(→(→)-\s\up8(→(→))-(\s\up8(→(→)-\s\up8(→(→))=________.
0 [法一:(\s\up8(→(→)-\s\up8(→(→))-(\s\up8(→(→)-\s\up8(→(→))=\s\up8(→(→)-\s\up8(→(→)-\s\up8(→(→)+\s\up8(→(→)=\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)=\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)=0.
法二:(\s\up8(→(→)-\s\up8(→(→))-(\s\up8(→(→)-\s\up8(→(→))=(\s\up8(→(→)-\s\up8(→(→))+\s\up8(→(→)-\s\up8(→(→)=\s\up8(→(→)+\s\up8(→(→)-\s\up8(→(→)=\s\up8(→(→)-\s\up8(→(→)=0.]
9.已知长方体ABCDA′B′C′D′,化简下列向量表达式,并标出化简结果的向量:
(1)\s\up8(→(→)-\s\up8(→(→);
(2)\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→);
(3)\s\up8(→(→)+\s\up8(→(→)-\s\up8(→(→).
[解] (1)\s\up8(→(→)-\s\up8(→(→)=\s\up8(→(→)+\s\up8(→(→)=\s\up8(→(→)+\s\up8(→(→)=\s\up8(→(→).
(2)\s\up8(→(→)+\s\up8(→(→)+\s\up8(→(→)=\s\up8(→(→).