Vector Algebra Question 288
Question: The points with position vectors $ 60,\mathbf{i}+3,\mathbf{j} $ , $ 40,\mathbf{i}-8\mathbf{j}, $ , $ a,\mathbf{i}-52,\mathbf{j} $ are collinear, if $ a= $
[RPET 1991; IIT 1983; MP PET 2002]
Options:
A) 40
B) 40
C) 20
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- If the given points be A, B, C, then $ \overrightarrow{AB}=k(\overrightarrow{BC}) $
$ \Rightarrow -20\mathbf{i}-11\mathbf{j}=k[ (a-40)\mathbf{i}-44\mathbf{j} ] $ On comparing, $ -11=-44k\Rightarrow k=\frac{1}{4} $ And $ -20=\frac{1}{4}(a-40)\Rightarrow a=-40. $
BETA
