A) \[\alpha =2,\,\,\beta =1\]
B) \[\alpha =1,\,\,\beta =1\]
C) \[\alpha =2,\,\,\beta =2\]
D) \[\alpha =1,\,\,\beta =2\]
Correct Answer: B
Solution :
\[\because \] \[\vec{a},\vec{b}\] and \[\vec{c}\] are coplanar. \[\Rightarrow \] \[[\vec{a}\,\,\vec{b}\,\,\vec{c}]=0\Rightarrow \alpha +\beta =2\] ? (i) Also \[\vec{a}\] bisects the angle between \[\vec{b}\] and \[\vec{c}\] \[\Rightarrow \,\vec{a}=\lambda \left( \hat{b}+\hat{c} \right)\Rightarrow \vec{a}=\lambda \left( \frac{\hat{i}+2\hat{j}+\hat{k}}{\sqrt{2}} \right)\] ? (ii) Comparing (ii) with \[\vec{a}=\alpha \,\hat{i}+2\hat{j}+\beta \hat{k}\], we get \[\lambda =\sqrt{2},\,\,\therefore \alpha =1\] and \[\beta =1\], which also satisfies (i)You need to login to perform this action.
You will be redirected in
3 sec