A) All values of m
B) \[m<-2\]or \[m>-1/2\]
C) \[m=-1/2\]
D) \[m\in \left[ -2,-\frac{1}{2} \right]\]
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 \[\vec{a}.\vec{b}>0\] \[\Rightarrow 2(1+m)+2{{m}^{2}}+3m>0\Rightarrow 2{{m}^{2}}+5m+2>0\] \[\Rightarrow 2{{m}^{2}}+4m+m+2>0\Rightarrow (2m+1)(m+2)>0\] \[\Rightarrow m<-2\] or \[m>-\frac{1}{2}\]
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