In-a-parallelogram-OABC-OA-a-OC-c-D-is-a-point-such-that-AD-DB-1-2-Express-the-following-in-terms-of-a-and-c-i-CB-ii-BC-iii-AB-iv-AD-v-OD-vi-DC-

Question Number 72832 by necxxx last updated on 03/Nov/19

I n a p a r a l l e l o g r a m O A B C, O \overset{⇁}{A} = \overset{- ⇁}{a},

O \vec{C} = \vec{c}, D i s a p o i n t s u c h t h a t A \vec{D} : D \vec{B} = 1 : 2

E x p r e s s t h e f o l l o w i n g i n t e r m s o f a a n d c

(i) C \vec{B} (i i) B \vec{C} (i i i) A \vec{B} (i v) A \vec{D} (v) O \vec{D}

(v i) D \vec{C}

Commented by necxxx last updated on 03/Nov/19

p l e a s e h e l p . T h a n k s i n a d v a n c e .

Answered by mind is power last updated on 03/Nov/19

C \vec{B} = O \vec{A} = \vec{a}

B \vec{C} = - C \vec{B} = - \vec{a}

A \vec{B} = O \vec{C} = \vec{c}

A \vec{D} = \frac{1}{2} . D \vec{B}

A \vec{D} + D \vec{B} = A \vec{B}

3 A \vec{D} = A \vec{B} \Rightarrow A \vec{D} = \frac{A \vec{B}}{3} = \frac{\vec{c}}{3}

O \vec{D} = O \vec{A} + A \vec{D} = \vec{a} + \frac{\vec{c}}{3}

Commented by necxxx last updated on 03/Nov/19

I n o w g e t i t . T h a n k y o u s o m u c h s i r

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