=(6,1),
=(x,y),
=(-2,-3).
图3
(1)若
∥
,求x与y间的关系式;
(2)若又有
⊥
,求x,y的值及四边形ABCD的面积.
=(6,1),=(x,y),=(-2,-3).
图3
(1)若∥,求x与y间的关系式;
(2)若又有⊥,求x,y的值及四边形ABCD的面积.
=++=(x+4,y-2),=-=(-x-4,2-y),又∥且
=(x,y),∴x(2-y)-y(-x-4)=0,即x+2y=0.①
(2)由于
=
+
=(x+6,y+1),
=
+
=(x-2,y-3),
又
⊥
,∴
·
=0,
即(x+6)(x-2)+(y+1)(y-3)=0.②
联立①②化简,得y2-2y-3=0,∴y=3或y=-1.
故当y=3时,x=-6,此时
=(0,4),
=(-8,0),
∴S四边形ABCD=
|
||
|=16;
当y=-1时,x=2,此时
=(8,0),
=(0,-4),∴S四边形ABCD=
|
||
|=16.
点评
:引入平面向量的坐标可使向量运算完全代数化,平面向量的坐标成了数与形结合的载体.