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填空题在直角坐标系下,向量在y轴上的射影是( )

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时间：2025-12-02 00:44:08

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已知四面体OABCD的顶点坐标O(0,0,0),A(1,-1,1),B(2,1,0),C(-1,1,1),则四面体体积为__________

已知空间的基向量<img src="https://tihai-oss-cloud.itihey.com/img/42c7f74dc935f270a6beb66cca59a5dc.png">则向量<img src="https://tihai-oss-cloud.itihey.com/img/c855e67942c96d0c29a4fe835522606f.png">的坐标是( )

点P(1,2,-1)关于坐标面yoz的对称点坐标是( ),关于y轴的对称点坐标是( )

向量<img src="https://tihai-oss-cloud.itihey.com/img/4a777bf30d075980843a9a1906a0c9e0.webp">在<img src="https://tihai-oss-cloud.itihey.com/img/b2c50712455fea8ce650ffc7e0970859.webp">上的射影是( )

在直角坐标系下,向量<img src="https://tihai-oss-cloud.itihey.com/img/0808dab8bb17f01738f633095ff8cd0c.webp">在y轴上的射影是( )

已知四面体ABCD的顶点坐标A(0,0,0),B(6,0,6),C(4,3,0),D(2,-1,3),则四面体的体积是( )

设M是平行四边形ABCD的中心,O是任意一点,则<img src="https://tihai-oss-cloud.itihey.com/img/9c2e1770b2cf2c17f238313d883113a9.webp">

A. <img src="https://tihai-oss-cloud.itihey.com/img/72d7b28caca660953dc26518e59064f7.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/567997b92548f5684a94340bb9a32808.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/28d5e43a8e6acea4aa2365051b4c14d1.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/bbd0e2ff7e131864dc77be59fe2ad3ca.webp">

设<img src="https://tihai-oss-cloud.itihey.com/img/acc672322a9ceddb42feaf9ce58c3240.webp">是三向量,则下列条件不是三向量共面的充分必要条件的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/23e23276175409c6bfff1fef1cab1f71.png">,其中l,m,n为不全为零的常数B. <img src="https://tihai-oss-cloud.itihey.com/img/505f03c103683df6295d2a11e509c053.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/01b99b00339241fcc24936fac9e356a1.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/8e38e36f65460531286501caef909246.webp">共面

在直角坐标系中,已知三点A(-2,1,4),B(-2,-3,-4),C(-1,3,3),则三角形ABC的面积为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/9d1cb885973ac62957ae63e33f0958c1.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/325351287e86c63bb5cd48d8f963e58b.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/1b7290c0778ee106191d617a84c5741c.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/f394f489c06673bf62d53acb5bb91c93.webp">

已知向量<img src="https://tihai-oss-cloud.itihey.com/img/fad51e5addae65a92597220edb8d95d4.webp">与单位向量<img src="https://tihai-oss-cloud.itihey.com/img/72291121c9f796a385e6c263b400dcb1.webp">的夹角是<img src="https://tihai-oss-cloud.itihey.com/img/0ee682f94b143dc5fe321d32f1e2f323.webp">,且<img src="https://tihai-oss-cloud.itihey.com/img/f8ffcf2caecb34e51cb650c34034255b.webp">,则<img src="https://tihai-oss-cloud.itihey.com/img/5658762bb7df5974a92697b79434dc1a.webp">为( )

A. -5B. 5C. <img src="https://tihai-oss-cloud.itihey.com/img/2446ba9e875b66fefca928ae5ae3bbbe.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/0c9d1eed9557a48379403c24d719eef3.webp">

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