CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The position vectors of $$A$$ and $$B$$ are $$2\hat{i}+2\hat{j}+\hat{k}$$ and $$2\hat{i}+4\hat{j}+4\hat{k}.$$ The length of the internal bisector of $$\angle BOA$$ of the triangle $$AOB$$ is


A
1369
loader
B
1399
loader
C
203
loader
D
2179
loader

Solution

The correct option is B $$\displaystyle \sqrt { \dfrac { 136 }{ 9 }  } $$
Here $$OA=3,OB=6$$
$$\therefore$$ Internal bisector $$OD$$ divides $$AB$$ in the ratio $$1:2$$
$$\Rightarrow$$ Position vector of $$D$$ is $$\displaystyle \left( 2,\frac { 8 }{ 3 } ,2 \right) $$

$$\displaystyle \therefore \left| OD \right| =\sqrt { 4+\dfrac { 64 }{ 9 } +4 } =\sqrt { \dfrac { 136 }{ 9 }  } $$

471251_37385_ans.PNG

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image