Vector Algebra Question 293
Question: Three points whose position vectors are $ \mathbf{a}+\mathbf{b},\mathbf{a}-\mathbf{b} $ and $ \mathbf{a}+k\mathbf{b} $ will be collinear, if the value of k is
[IIT 1984]
Options:
A) Zero
B) Only negative real number
C) Only positive real number
D) Every real number
Show Answer
Answer:
Correct Answer: D
Solution:
- $ \overrightarrow{AB}=\lambda \overrightarrow{BC} $ , (for collinearity) Here $ \overrightarrow{AB}=-2\mathbf{b}, $ $ \overrightarrow{BC}=(k+1)\mathbf{b} $ Hence $ \forall k\in R\Rightarrow \overrightarrow{AB}=\lambda \overrightarrow{BC}. $
BETA
