Question

如圖，設(shè)點(diǎn)P、Q是線段AB的三等分點(diǎn)，若

OA

=a，

OB

=b，則

OP

=（　　）用a、b表示．

• A、-

  2

  3

  a

  +

  1

  3

  b

• B、

  1

  3

  b

  +

  2

  3

  a

• C、

  1

  2

  a

  +

  1

  3

  b

• D、

  1

  3

  a

  -

  2

  3

  b

Answer 1

分析：由已知

OA

=a，

OB

=b，及向量加法的三角形法可得

OP

=

OA

+

AP

=

OA

+

1

3

AB

=

OA

+

1

3

(

OB

-

OA

)=

1

3

OB

+

2

3

OA

，把已知代入可求．

解答：解：∵

OA

=a，

OB

=b，
由向量加法的三角形法則可得

OP

=

OA

+

AP

=

OA

+

1

3

AB

=

OA

+

1

3

(

OB

-

OA

)
=

1

3

OB

+

2

3

OA

=

1

3

b

+

2

3

a

故選B．

點(diǎn)評(píng)：本題主要注意靈活應(yīng)用向量加法，減法的三角形法則及向量共線定理，靈活利用向量的知識(shí)是解決本題的關(guān)鍵．