优优班--学霸训练营 > 知识点挑题
全部资源
          排序:
          最新 浏览

          50条信息

            • 1. 已知 \(a\)\(=(2,-1,3)\), \(b\)\(=(-1,4,-2)\), \(c\)\(=(7,5, \)\(λ\)\()\),若 \(a\)\(b\)\(c\)三向量共面,则实数 \(λ\)等于(    )
              A.\( \dfrac{62}{7}\)                    
              B.\(9\)
              C.\( \dfrac{64}{7}\)                        
              D.\( \dfrac{65}{7}\)
            • 2.

              已知斜三棱柱\(ABC-{{A}_{1}}{{B}_{1}}{{C}_{1}}\),\(\angle BCA=90{}^\circ \),\(AC=BC=2\),\({{A}_{1}}\)在底面\(ABC\)上的恰为\(AC\)的中点\(D\),又知\(B{{A}_{1}}\bot A{{C}_{1}}\).

              \((\)Ⅰ\()\)求证:\(A{{C}_{1}}\bot \)平面\({{A}_{1}}BC\);

              \((\)Ⅱ\()\)求二面角\(A-{{A}_{1}}B-C\)的余弦值\(.\)                                                          

            • 3.

              \(①\)如果\(\overrightarrow{OP}= \dfrac{1}{2}\overrightarrow{OA}-\overrightarrow{OB}+ \dfrac{3}{2}\overrightarrow{OC}.\) 则\(P\),\(A\),\(B\),\(C\)四点共面\(;\)

              \(②\)若向量\(e_{1}\),\(e_{2}\),\(e_{3}\)是三个不共面的向量,且满足等式\(k_{1}e_{1}+k_{2}e_{2}+k_{3}e_{3}=0\),则\(k_{1}=k_{2}=k_{3}=0\).

              \(③\)已知空间向量\(a\),\(b\),\(c\),则对于空间的任意一个向量\(p\)总存在实数\(x\),\(y\),\(z\)使得\(p=xa+yb+zc\).

              \(④\)若\(p=xa+yb\),则\(p\)与\(a\),\(b\)共面;

              其中是真命题的序号是________\((\)把所有真命题的序号都填上\()\).

            • 4.
              正方体\(ABCD-A\)\({\,\!}_{1}\) \(B\)\({\,\!}_{1}\) \(C\)\({\,\!}_{1}\) \(D\)\({\,\!}_{1}\) 的棱长为\(1\),若动点\(P\)在线段\(BD\)\({\,\!}_{1}\) 上运动,则\(\overrightarrow{DC}\) \(·\)\(\overrightarrow{AP}\) 的取值范围是________.
            • 5. 已知点\(P\)为三棱锥\(O-ABC\)的底面\(ABC\)所在平面内的一点,且\( \overrightarrow{OP}= \dfrac {1}{2} \overrightarrow{OA}+k \overrightarrow{OB}- \overrightarrow{OC}\),则实数\(k\)的值为\((\)  \()\)
              A.\(- \dfrac {1}{2}\)
              B.\( \dfrac {1}{2}\)
              C.\(1\)
              D.\( \dfrac {3}{2}\)
            • 6.

              下列命题中,正确命题的个数为(    )

              \(①\)若\(\overrightarrow{a}\parallel \overrightarrow{b}\),则\(\overrightarrow{a}\)与\(\overrightarrow{b}\)方向相同或相反;

              \(②\)若\(\overrightarrow{AB}=\overrightarrow{CD}\),则\(A\),\(B\),\(C\),\(D\)四点共线;

              \(③\)若\(\overrightarrow{a}\),\(\overrightarrow{b}\)不共线,则空间任一向量\(\overrightarrow{p}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}(λμ∈R)\).

              A.\(0\)
              B.\(1\)
              C.\(2\)
              D.\(3\)
            • 7.

              给出下列命题正确命题个数是

              \(①\)已知\(a⊥b\),则\(a·(b+c)+c·(b-a)=b·c\);

              \(②A\),\(B\),\(M\),\(N\)为空间四点,若\( \overset{→}{BA} \),\( \overset{→}{BM} \),\( \overset{→}{BN} \)不构成空间的一个基底,则\(A\),\(B\),\(M\),\(N\)共面;

              \(③\)已知\(a⊥b\),则\(a\),\(b\)与任何向量不构成空间的一个基底;

              \(④\)已知\(\{a,b,c\}\)是空间的一个基底,则基向量\(a\),\(b\)可以与向量\(m=a+c\)构成空间另一个基底.

              A.\(1\)
              B.\(2\)
              C.\(3\)
              D.\(4\)
            • 8.

              已知\(A\)、\(B\)、\(C\)、\(D\)四点共面且任三点不共线,面外空间一点\(P\)满足\(\overrightarrow{AP}=x\overrightarrow{PB}+y\overrightarrow{PC}+z\overrightarrow{PD}\),则\(x+y+z=(\)   \()\)

              A.\(-1\)
              B.\(0\)
              C.\(3\)
              D.\(1\)
            • 9.

              已知平行六面体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)中,底面\(ABCD\)是边长为\(2\)的正方形,侧棱\(AA_{1}\)的长为\(2\),\(∠A_{1}AB=∠A_{1}AD=120^{\circ}\).



              \((1)\)求:对角线\(AC_{1}\)的长;

              \((2)\)求:直线\(AC_{1}\)和\(BB_{1}\)的夹角的余弦值.

            • 10.

              如图,在四面体\(ABCD\)中,已知\(\overrightarrow{AB}=b\),\(\overrightarrow{AD}=a\),\(\overrightarrow{AC}\)\(=\)\(c\)\(\overrightarrow{BE}=\dfrac{1}{2}\overline{EC}\),则\(\overrightarrow{DE}\)等于                 \((\)  \()\).




              A.\(-a+\dfrac{2}{3}b+\dfrac{1}{3}c\)
              B.\(a+\dfrac{2}{3}b+\dfrac{1}{3}c\)

              C.\(a-\dfrac{2}{3}b+\dfrac{1}{3}c\)
              D.\(\dfrac{2}{3}a-b+\dfrac{1}{3}c\)
            0/40

            进入组卷