Vector Algebra Question 337
Question: If three points A, B, C are collinear, whose position vectors are $ \mathbf{i}-2\mathbf{j}-8\mathbf{k},5\mathbf{i}-2\mathbf{k} $ and $ 11,\mathbf{i}+,3,\mathbf{j}+7\mathbf{k} $ respectively, then the ratio in which B divides AC is
[RPET 1999]
Options:
A) 1 : 2
B) 2 : 3
C) 2 : 1
D) 1 : 1
Show Answer
Answer:
Correct Answer: B
Solution:
- Let the B divide AC in ratio $ \lambda :1 $ , then $ 5\mathbf{i}-2\mathbf{k}=\frac{\lambda (11\mathbf{i}+3\mathbf{j}+7\mathbf{k})+\mathbf{i}-2\mathbf{j}-8\mathbf{k}}{\lambda +1} $
$ \Rightarrow 3\lambda -2=0 $
$ \Rightarrow \lambda =\frac{2}{3} $ i.e., ratio = 2 : 3.
BETA
