共50条信息
三棱锥\(A-BCD\)中,\(AB=AC=AD=2\),\(∠BAD=90^{\circ}\),\(∠BAC=60^{\circ}\),则\(\overrightarrow{AB}\)\(·\)\(\overrightarrow{CD}\)等于\((\) \()\)
如图,在三棱柱\(ABC-A_{1}B_{1}C_{1}\)中,\(M\)为\(A_{1}C_{1}\)的中点,若\(\overrightarrow{AB}=\overrightarrow{a}\),\(\overrightarrow{BC}=\overrightarrow{b}\),\(\overset{⇀}{A{A}_{1}}= \overset{⇀}{c} \),则\(\overrightarrow{BM}\)可表示为\((\) \()\)
在平行六面体\(ABCD-A_{1}B_{1}C_{1}D_{1}\) 中,设\( \overrightarrow{A{C}_{1}}=x \overrightarrow{AB}+2y \overrightarrow{BC}+3z \overrightarrow{C{C}_{1}} \),则\(x{+}y{+}z=(\) \()\)
如图,以长方体\(ABCD-{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\)的顶点\(D\)为坐标原点,过点\(D\)的三条棱所在直线为坐标轴建立空间直角坐标系\(.\) 若\(\overrightarrow{D{{B}_{1}}}\)的坐标为\(\left(3,4,5\right) \),则\(\overrightarrow{{{A}_{1}}C}\)的坐标是
如图所示,在平行六面体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中,设\( \overrightarrow{A{A}_{1}}= \overrightarrow{a} \),\( \overrightarrow{AB}= \overrightarrow{b} \),\( \overrightarrow{AD}= \overrightarrow{c} \),\(M\),\(N\),\(P\)分别是\(AA_{1}\),\(BC\),\(C_{1}D_{1}\)的中点,则\( \overrightarrow{MP}+ \overrightarrow{N{C}_{1}}= =(\) \()\)
如图所示,空间四边形\(OABC\)中,\(\overrightarrow{OA}=a\),\(\overrightarrow{OB}=b\),\(\overrightarrow{OC}=c\),点\(M\)在\(OA\)上,且\(OM=2MA\),点\(N\)为\(BC\)的中点,则\(\overrightarrow{MN}\)等于\((\) \()\)
已知向量\( \overrightarrow{a}=m \overrightarrow{i}+5 \overrightarrow{j}- \overrightarrow{k}, \overrightarrow{b}=3 \overrightarrow{i}+ \overrightarrow{j}+r \overrightarrow{k} \),若\( \overrightarrow{a} /\!/ \overrightarrow{b} \)则实数\(m\)\(= \)______,\(r\)\(= \)______.
在四面体\(ABCD\)中,\(E\),\(G\)分别是\(CD\),\(BE\)的中点,若空间向量\( \overset{→}{AG}=x \overset{→}{AB}+y \overset{→}{AD}+z \overset{→}{AC} \),则\(x+y+z=\)( )
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