Vector Algebra Question 249
Question: A and B are two points. The position vector of A is $ 6\mathbf{b}-2\mathbf{a}. $ A point P divides the line AB in the ratio 1 : 2. If $ \mathbf{a}-\mathbf{b} $ is the position vector of P, then the position vector of B is given by
[MP PET 1993]
Options:
A) $ 7\mathbf{a}-15\mathbf{b} $
B) $ 7\mathbf{a}+15\mathbf{b} $
C) $ 2\pi /3 $
D) $ 15\mathbf{a}+7\mathbf{b} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \overrightarrow{OP}=\frac{1(\overrightarrow{OB})+2(6\mathbf{b}-2\mathbf{a})}{1+2} $
$ \Rightarrow 3(\mathbf{a}-\mathbf{b})=\overrightarrow{OB}+12\mathbf{b}-4\mathbf{a} $
$ \Rightarrow \overrightarrow{OB}=7\mathbf{a}-15\mathbf{b} $ .
BETA
