A) \[\mathbf{a}-\mathbf{b}\]
B) \[\mathbf{a}+\mathbf{b}\]
C) \[\mathbf{a}\times \mathbf{b}+\mathbf{a}\]
D) \[\mathbf{a}\times \mathbf{b}+\mathbf{b}\]
Correct Answer: B
Solution :
\[\mathbf{r}\times \mathbf{a}-\mathbf{b}\times \mathbf{a}=0\] and \[\mathbf{r}\times \mathbf{b}+\mathbf{b}\times \mathbf{a}=0\] Adding, we get \[\mathbf{r}\times (\mathbf{a}+\mathbf{b})=0\] But as we are given \[\mathbf{a}\ne \lambda \,\mathbf{b},\] therefore \[\mathbf{r}=\mathbf{a}+\mathbf{b}.\]You need to login to perform this action.
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