A) \[3\lambda +2\mu =0\]
B) \[3\lambda =2\mu \]
C) \[\lambda =\mu \]
D) \[\lambda +\mu =0\]
Correct Answer: B
Solution :
[b] \[3\lambda \vec{c}+2\mu (\vec{a}\times \vec{b})=0\] \[\Rightarrow 3\lambda \vec{c}=-2\mu (\vec{a}\times \vec{b})\] So, one possibility is \[\vec{c}\] and \[(\vec{a}\times \vec{b})\] are non-collinear. \[\Rightarrow 3\lambda =2\mu \]
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