Vector Algebra Question 233
Question: If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that $ \overrightarrow{AC}=3\overrightarrow{AB} $ is
[MNR 1980; MP PET 1995, 99]
Options:
A) $ 3\mathbf{a}-\mathbf{b} $
B) $ 3\mathbf{b}-\mathbf{a} $
C) $ 3\mathbf{a}-2\mathbf{b} $
D) $ 3\mathbf{b}-2\mathbf{a} $
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Answer:
Correct Answer: D
Solution:
- Since given that $ \overrightarrow{AC}=3\overrightarrow{AB}. $ It means that point $ C $ divides $ AB $ externally. Thus $ \overrightarrow{AC}:\overrightarrow{BC}=3:2 $ Hence $ \overrightarrow{OC}=\frac{3.\mathbf{b}-2.\mathbf{a}}{3-2}=3\mathbf{b}-2\mathbf{a}. $
BETA
