Trong không gian Oxyz, cho hai vectơ u → = ( 3 ; 2 ; − 2 ) , v → = ( − 1 ; 1 ; 4 ) \overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right) u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 3 ; 2 ; − 2 ) , v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( − 1 ; 1 ; 4 ) . Tính tích vô hướng của hai vectơ đó.

( 10 ; − 10 ; 5 ) \left(10;-10;5\right) ( 1 0 ; − 1 0 ; 5 )

( − 10 ; 10 ; − 5 ) \left(-10;10;-5\right) ( − 1 0 ; 1 0 ; − 5 )

Trong không gian Oxyz, cho hai vectơ u → = ( 3 ; 2 ; − 2 ) , v → = ( − 1 ; 1 ; 4 ) \overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right) u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 3 ; 2 ; − 2 ) , v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( − 1 ; 1 ; 4 ) . Tính tích có hướng của hai vectơ đó.

( 10 ; − 10 ; 5 ) \left(10;-10;5\right) ( 1 0 ; − 1 0 ; 5 )

( − 10 ; 10 ; − 5 ) \left(-10;10;-5\right) ( − 1 0 ; 1 0 ; − 5 )

Trong không gian Oxyz, cho ba vectơ u → = ( 3 ; 2 ; − 2 ) , v → = ( − 1 ; 1 ; 4 ) , w → = ( 2 ; 0 ; − 2 ) \overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right),\ \overrightarrow{w\ }=\left(2;0;-2\right) u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 3 ; 2 ; − 2 ) , v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( − 1 ; 1 ; 4 ) , w <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> = ( 2 ; 0 ; − 2 ) . Tính tích hỗn tạp [ u → , v → ] . w → \left[\overrightarrow{u\ },\overrightarrow{v\ }\right].\overrightarrow{w\ } [ u <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> , v <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> ] . w <path d="M0 241v40h399891c-47.3 35.3-84 78-110 128 -16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85 -40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5 -12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z"> .

( 20 ; 30 ; 20 ) \left(20;30;20\right) ( 2 0 ; 3 0 ; 2 0 )

( − 20 ; − 30 ; − 20 ) \left(-20;-30;-20\right) ( − 2 0 ; − 3 0 ; − 2 0 )

Trong không gian Oxyz , cho hình bình hành ABCD có A ( 2 ; 1 ; − 1 ; ) , B ( − 3 ; 1 ; 0 ) , C ( 2 ; 4 ; − 3 ) A\left(2;1;-1;\right),\ B\left(-3;1;0\right),C\left(2;4;-3\right) A ( 2 ; 1 ; − 1 ; ) , B ( − 3 ; 1 ; 0 ) , C ( 2 ; 4 ; − 3 ) . Tìm tọa độ đỉnh D ?

( 7 ; 4 ; − 4 ) \left(7;4;-4\right) ( 7 ; 4 ; − 4 )

( − 3 ; − 2 ; 2 ) \left(-3;-2;2\right) ( − 3 ; − 2 ; 2 )

( − 7 ; − 4 ; 4 ) \left(-7;-4;4\right) ( − 7 ; − 4 ; 4 )

( 3 ; 2 ; − 2 ) \left(3;2;-2\right) ( 3 ; 2 ; − 2 )

Trong không gian Oxyz , cho hình bình hành ABCD có A ( 2 ; 1 ; − 1 ; ) , B ( − 3 ; 1 ; 0 ) , C ( 2 ; 4 ; − 3 ) A\left(2;1;-1;\right),\ B\left(-3;1;0\right),C\left(2;4;-3\right) A ( 2 ; 1 ; − 1 ; ) , B ( − 3 ; 1 ; 0 ) , C ( 2 ; 4 ; − 3 ) . Tính diện tích hình bình hành đó?

334 \sqrt{334} 3 3 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

334 2 \frac{\sqrt{334}}{2} 2 3 3 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

443 \sqrt{443} 4 4 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

443 2 \frac{\sqrt{443}}{2} 2 4 4 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Trong không gian Oxyz , cho tam giác ABC có A ( 0 ; 1 ; − 1 ) , B ( 0 ; 5 ; 0 ) , C ( 4 ; 1 ; 2 ) A\left(0;1;-1\right),\ B\left(0;5;0\right),C\left(4;1;2\right) A ( 0 ; 1 ; − 1 ) , B ( 0 ; 5 ; 0 ) , C ( 4 ; 1 ; 2 ) . Tính diện tích tam giác đó?

2 26 2\sqrt{26} 2 2 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 26 4\sqrt{26} 4 2 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

4 11 4\sqrt{11} 4 1 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 11 2\sqrt{11} 2 1 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Trong không gian Oxyz , cho hình hộp ABCD.A'B'C'D' có A ( 3 ; 1 ; 0 ) , B ( − 2 ; 0 ; 5 ) , D ( 4 ; 1 ; 2 ) , A ′ ( 2 ; − 2 ; 2 ) A\left(3;1;0\right),\ B\left(-2;0;5\right),\ D\left(4;1;2\right),\ A'\left(2;-2;2\right) A ( 3 ; 1 ; 0 ) , B ( − 2 ; 0 ; 5 ) , D ( 4 ; 1 ; 2 ) , A ′ ( 2 ; − 2 ; 2 ) . Tính thể tích khối hộp đó?

41 \sqrt{41} 4 1 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

TÍCH CÓ HƯỚNG CỦA HAI VECTƠ

Authored by HỒNG NGUYỄN

Mathematics

12th Grade

Used 11+ times

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10 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Trong không gian Oxyz, cho hai vectơ $\overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right)$ . Tính tích vô hướng của hai vectơ đó.

$\left(10;-10;5\right)$

$\left(-10;10;-5\right)$

$-9$

$9$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Trong không gian Oxyz, cho hai vectơ $\overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right)$ . Tính tích có hướng của hai vectơ đó.

$\left(10;-10;5\right)$

$\left(-10;10;-5\right)$

$-9$

$9$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Trong không gian Oxyz, tích có hướng của hai vectơ cho kết quả là

một vectơ

một số

MULTIPLE CHOICE QUESTION

$-36$

$36$

$6$

$-6$

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Trong không gian Oxyz, cho hình hộp ABCD.A'B'C'D' có $A\left(3;1;0\right),\ B\left(-2;0;5\right),\ D\left(4;1;2\right),\ A'\left(2;-2;2\right)$ . Tính thể tích khối hộp đó?

$\sqrt{41}$

$41$

$\frac{41}{6}$

$\frac{41}{3}$

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TÍCH CÓ HƯỚNG CỦA HAI VECTƠ

Trong không gian Oxyz, cho hai vectơ u →=(3;2;−2), v →=(−1;1;4)\overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right)u =(3;2;−2), v =(−1;1;4) . Tính tích vô hướng của hai vectơ đó.

Trong không gian Oxyz, cho hai vectơ u →=(3;2;−2), v →=(−1;1;4)\overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right)u =(3;2;−2), v =(−1;1;4) . Tính tích có hướng của hai vectơ đó.

Trong không gian Oxyz, tích có hướng của hai vectơ cho kết quả là

Trong không gian Oxyz, tích vô hướng của hai vectơ cho kết quả là

Trong không gian Oxyz, cho hình bình hành ABCD có A(2;1;−1;), B(−3;1;0),C(2;4;−3)A\left(2;1;-1;\right),\ B\left(-3;1;0\right),C\left(2;4;-3\right)A(2;1;−1;), B(−3;1;0),C(2;4;−3) . Tìm tọa độ đỉnh D?

Trong không gian Oxyz, cho hình bình hành ABCD có A(2;1;−1;), B(−3;1;0),C(2;4;−3)A\left(2;1;-1;\right),\ B\left(-3;1;0\right),C\left(2;4;-3\right)A(2;1;−1;), B(−3;1;0),C(2;4;−3) . Tính diện tích hình bình hành đó?

Trong không gian Oxyz, cho tam giác ABC có A(0;1;−1), B(0;5;0),C(4;1;2)A\left(0;1;-1\right),\ B\left(0;5;0\right),C\left(4;1;2\right)A(0;1;−1), B(0;5;0),C(4;1;2) . Tính diện tích tam giác đó?

Trong không gian Oxyz, cho tứ diện ABCD có A(0;1;−1), B(0;5;0),C(4;1;2), D(2;−2;2)A\left(0;1;-1\right),\ B\left(0;5;0\right),C\left(4;1;2\right),\ D\left(2;-2;2\right)A(0;1;−1), B(0;5;0),C(4;1;2), D(2;−2;2) . Tính thể tích tứ diện đó?

Trong không gian Oxyz, cho hình hộp ABCD.A'B'C'D' có A(3;1;0), B(−2;0;5), D(4;1;2), A′(2;−2;2)A\left(3;1;0\right),\ B\left(-2;0;5\right),\ D\left(4;1;2\right),\ A'\left(2;-2;2\right)A(3;1;0), B(−2;0;5), D(4;1;2), A′(2;−2;2) . Tính thể tích khối hộp đó?

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Trong không gian Oxyz, cho hai vectơ $\overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right)$ . Tính tích vô hướng của hai vectơ đó.

Trong không gian Oxyz, cho hai vectơ $\overrightarrow{u\ }=\left(3;2;-2\right),\ \overrightarrow{v\ }=\left(-1;1;4\right)$ . Tính tích có hướng của hai vectơ đó.

Trong không gian Oxyz, cho hình bình hành ABCD có $A\left(2;1;-1;\right),\ B\left(-3;1;0\right),C\left(2;4;-3\right)$ . Tìm tọa độ đỉnh D?

Trong không gian Oxyz, cho hình bình hành ABCD có $A\left(2;1;-1;\right),\ B\left(-3;1;0\right),C\left(2;4;-3\right)$ . Tính diện tích hình bình hành đó?

Trong không gian Oxyz, cho tam giác ABC có $A\left(0;1;-1\right),\ B\left(0;5;0\right),C\left(4;1;2\right)$ . Tính diện tích tam giác đó?

Trong không gian Oxyz, cho tứ diện ABCD có $A\left(0;1;-1\right),\ B\left(0;5;0\right),C\left(4;1;2\right),\ D\left(2;-2;2\right)$ . Tính thể tích tứ diện đó?

Trong không gian Oxyz, cho hình hộp ABCD.A'B'C'D' có $A\left(3;1;0\right),\ B\left(-2;0;5\right),\ D\left(4;1;2\right),\ A'\left(2;-2;2\right)$ . Tính thể tích khối hộp đó?