问题 选择题
△ABC中,AB边的高为CD,若
CB
=
a
CA
=
b
a
b
=0,|
a
|=1,|
b
|=2,则
AD
=(  )
A.
1
3
a
-
1
3
b
B.
2
3
a
-
2
3
b
C.
3
5
a
-
3
5
b
D.
4
5
a
-
4
5
b
答案

a
b
=0,

∴CA⊥CB

∵CD⊥AB

∵|

a
|=1,|
b
|=2

∴AB=

5

由射影定理可得,AC2=AD•AB

AD=

4
5
=
4
5
5

AD
AB
=
4
5
5
5
=
4
5

AD
=
4
5
AB
=
4
5
(
CB
-
CA
)
=
4
5
(
a
-
b
)

故选D

多项选择题 X型题
单项选择题