四边形ABCD中,向量AB=(x,3),向量BC=(2,-1),向量CD=(-4,y).(1)若向量AB//向量DA,试求x与y满足的关系式;(2)满足(1)的同时又有向量AC垂直于向量BD,求x,y的值及四边形ABCD的面积.
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![四边形ABCD中,向量AB=(x,3),向量BC=(2,-1),向量CD=(-4,y).(1)若向量AB//向量DA,试求x与y满足的关系式;(2)满足(1)的同时又有向量AC垂直于向量BD,求x,y的值及四边形ABCD的面积.](/uploads/image/z/10739621-29-1.jpg?t=%E5%9B%9B%E8%BE%B9%E5%BD%A2ABCD%E4%B8%AD%2C%E5%90%91%E9%87%8FAB%3D%28x%2C3%29%2C%E5%90%91%E9%87%8FBC%3D%282%2C-1%29%2C%E5%90%91%E9%87%8FCD%3D%28-4%2Cy%29.%EF%BC%881%EF%BC%89%E8%8B%A5%E5%90%91%E9%87%8FAB%2F%2F%E5%90%91%E9%87%8FDA%2C%E8%AF%95%E6%B1%82x%E4%B8%8Ey%E6%BB%A1%E8%B6%B3%E7%9A%84%E5%85%B3%E7%B3%BB%E5%BC%8F%EF%BC%9B%EF%BC%882%EF%BC%89%E6%BB%A1%E8%B6%B3%281%29%E7%9A%84%E5%90%8C%E6%97%B6%E5%8F%88%E6%9C%89%E5%90%91%E9%87%8FAC%E5%9E%82%E7%9B%B4%E4%BA%8E%E5%90%91%E9%87%8FBD%2C%E6%B1%82x%2Cy%E7%9A%84%E5%80%BC%E5%8F%8A%E5%9B%9B%E8%BE%B9%E5%BD%A2ABCD%E7%9A%84%E9%9D%A2%E7%A7%AF.)
四边形ABCD中,向量AB=(x,3),向量BC=(2,-1),向量CD=(-4,y).(1)若向量AB//向量DA,试求x与y满足的关系式;(2)满足(1)的同时又有向量AC垂直于向量BD,求x,y的值及四边形ABCD的面积.
四边形ABCD中,向量AB=(x,3),向量BC=(2,-1),向量CD=(-4,y).
(1)若向量AB//向量DA,试求x与y满足的关系式;(2)满足(1)的同时又有向量AC垂直于向量BD,求x,y的值及四边形ABCD的面积.
四边形ABCD中,向量AB=(x,3),向量BC=(2,-1),向量CD=(-4,y).(1)若向量AB//向量DA,试求x与y满足的关系式;(2)满足(1)的同时又有向量AC垂直于向量BD,求x,y的值及四边形ABCD的面积.
AB=(x,3),DA=(2-x,-y-2)
因为向量AB//向量DA
所以x(y+2)=3(x-2)
xy+2x=3x-6
xy-x=6
y=6/(x-1)
AC=(x+2,2),BD(-2,y-1)
因为向量AC垂直于向量BD
所以-2(x+2)+2(y-1)=0
x+2=y-1
x=y-3
因为y=6/(x-1)
所以y=6/(y-4)
(1)AB=(x,3),DA=(2-x,-y-2)
因为向量AB//向量DA
所以x(y+2)=3(x-2)
xy+2x=3x-6
xy-x=6
y=6/(x-1)
(2)AC=(x+2,2),BD(-2,y-1)
因为向量AC垂直于向量BD
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(1)AB=(x,3),DA=(2-x,-y-2)
因为向量AB//向量DA
所以x(y+2)=3(x-2)
xy+2x=3x-6
xy-x=6
y=6/(x-1)
(2)AC=(x+2,2),BD(-2,y-1)
因为向量AC垂直于向量BD
所以-2(x+2)+2(y-1)=0
x+2=y-1
x=y-3
因为y=6/(x-1)
所以y=6/(y-4)
然后你自己做吧,我这不太好写
收起
(1) X(Y+2)-(X-2)3=0 化一下即可
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