(\s\up6(→(→)-\s\up6(→(→))-(\s\up6(→(→)-\s\up6(→(→))=\s\up6(→(→)-\s\up6(→(→)-\s\up6(→(→)+\s\up6(→(→)
=\s\up6(→(→)+\s\up6(→(→)+\s\up6(→(→)+\s\up6(→(→)=\s\up6(→(→)+\s\up6(→(→)+\s\up6(→(→)+\s\up6(→(→)=0.
解法二:(利用向量的减法运算法则求解)
(\s\up6(→(→)-\s\up6(→(→))-(\s\up6(→(→)-\s\up6(→(→))=(\s\up6(→(→)-\s\up6(→(→))+\s\up6(→(→)-\s\up6(→(→)
=\s\up6(→(→)+\s\up6(→(→)-\s\up6(→(→)=\s\up6(→(→)-\s\up6(→(→)=0.
8.在平行六面体ABCD-A1B1C1D1中,若\s\up6(→(→)=x·\s\up6(→(→)+2y·\s\up6(→(→)+3z·\s\up6(→(→),则x+y+z=____.
[解析]
如图所示,有\s\up6(→(→)=\s\up6(→(→)+\s\up6(→(→)+\s\up6(→(→)=\s\up6(→(→)+\s\up6(→(→)+(-1)·\s\up6(→(→).
又∵\s\up6(→(→)=x·\s\up6(→(→)+2y·\s\up6(→(→)+3z·\s\up6(→(→),
∴,解得.
∴x+y+z=1+-=.
三、解答题
9.在四棱柱ABCD-A′B′C′D′中,底面ABCD为矩形,化简下列各式.
(1)\s\up6(→(→)+\s\up6(→(→)-\s\up6(→(→)+\s\up6(→(→)-\s\up6(→(→);
(2)\s\up6(→(→)-\s\up6(→(→)+\s\up6(→(→)-\s\up6(→(→).
[解析] (1)原式=\s\up6(→(→)+\s\up6(→(→)+\s\up6(→(→)-\s\up6(→(→)-\s\up6(→(→)=\s\up6(→(→).