Vector Algebra Question 122
Question: The vectors $ (2\hat{i}-m\hat{j}+3m\hat{k})\And $ $ {(1+m)\hat{i}-3m\hat{j}+\hat{k}} $ include an acute angle for
Options:
A) All values of m
B) $ m<-2 $ or $ m>-1/2 $
C) $ m=-1/2 $
D) $ m\in [ -2,-\frac{1}{2} ] $
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Answer:
Correct Answer: B
Solution:
- [b] $ \vec{a}=2\hat{i}-m\hat{j}+3m\hat{k} $ & $ \vec{b}=(1+m)\hat{i}-2m\hat{j}+\hat{k} $ and if angle between $ \vec{a} $ and $ \vec{b} $ is an acute, then $ \vec{a}.\vec{b}>0 $
$ \Rightarrow 2(1+m)+2m^{2}+3m>0\Rightarrow 2m^{2}+5m+2>0 $
$ \Rightarrow 2m^{2}+4m+m+2>0\Rightarrow (2m+1)(m+2)>0 $
$ \Rightarrow m<-2 $ or $ m>-\frac{1}{2} $
BETA
