Three Dimensional Geometry Question 396
Question: The vector $ \vec{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k} $ lies in the plane of the vectors $ \vec{b}=\hat{i}+\hat{j} $ and $ \vec{c}=\hat{j}+\hat{k} $ and bisects the angle between $ \vec{b} $ and $ \vec{c} $ . Then which one of the following gives possible values of a and b?
Options:
A) $ \alpha =2,\beta =2 $
B) $ \alpha =1,\beta =2 $
C) $ \alpha =2,\beta =1 $
D) $ \alpha =2,\beta =1 $
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Answer:
Correct Answer: D
Solution:
[d]
$ \therefore \vec{a} $ lies in the plane of $ \vec{b} $ and $ \vec{c} $
$ \therefore \vec{a}=\vec{b}+\lambda \vec{c} $
$ \Rightarrow \alpha \hat{i}+2\hat{j}+\beta \hat{k}=\hat{i}+\hat{j}+\lambda (\hat{j}+\hat{k}) $
$ \Rightarrow \alpha =1,2=1+\lambda ,\beta =\lambda \Rightarrow \alpha =1,\beta =1 $
BETA
