CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The vector $$\overrightarrow a  = \alpha \widehat i + 2\widehat j + \beta \widehat k$$ lies in the plane of the vectors $$\overrightarrow b  = \widehat i + \widehat j$$ and $$\overrightarrow c  = \widehat j + \widehat k$$ and bisects the angle between $$\overrightarrow b $$ and $$\overrightarrow c .$$ Then, which one of the following gives possible values of $$\alpha $$ and $$\beta ?$$


A
α=2,β=2
loader
B
α=1,β=2
loader
C
α=2,β=1
loader
D
α=1,β=1
loader

Solution

The correct option is D $$\alpha = 1,\,\beta = 1$$
$$\vec { a } =\lambda \left( \vec { b } +\vec { c }  \right) $$
$$(\because \vec { a } $$ lies in plane of $$\vec { b } $$ and $$\vec { c }$$ and bisects the angle between $$\vec { b }$$  and $$\vec { c } )$$
$$\Rightarrow \quad \alpha \vec { i } +2\vec { j } +\beta \vec { k } =\lambda \left( \cfrac { \vec { i } +\vec { j }  }{ \sqrt { 2 }  } +\cfrac { \vec { j } +\vec { k }  }{ \sqrt { 2 }  }  \right) $$
$$\Rightarrow \quad \alpha \vec { i } +2\vec { j } +\beta \vec { k } =\lambda \left( \cfrac { \vec { i } +2\vec { j } +\vec { k }  }{ \sqrt { 2 }  }  \right) $$
$$\Rightarrow \quad \lambda =\sqrt { 2 } \alpha \quad ,\quad \lambda =\sqrt { 2 } \quad and\quad \lambda =\sqrt { 2 } \beta $$
$$\therefore \quad \alpha =\beta =1$$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image