In $ riangle P Q R,(4 \hat{i}+3 \hat{j}+6 \hat{k}),(2 \hat{i}+2 \hat{j}+3 \hat{k})$ and $(3 \hat{i}+\hat{j}+3 \hat{k})$ are the position vectors of the vertices $\mathrm{P}, \mathrm{Q}$ and R respectively. Then the position vector of the point of intersection of the angle bisector of P with QR is

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In $	riangle P Q R,(4 \hat{i}+3 \hat{j}+6 \hat{k}),(2 \hat{i}+2 \hat{j}+3 \hat{k})$ and $(3 \hat{i}+\hat{j}+3 \hat{k})$ are the position vectors of the vertices $\mathrm{P}, \mathrm{Q}$ and R respectively. Then the position vector of the point of intersection of the angle bisector of P with QR is

Aicharya · Accepted Answer

$\begin{aligned} & P R=\sqrt{1+4+9}=\sqrt{14} \\ & P Q=\sqrt{4+1+9}=\sqrt{14} \\ & P R=P Q\end{aligned}$

$\triangle P Q R$ is isoceles triangle. Let $A$ be the position vector of point of intersection of angle bisector of angle $P$ and $Q R$. $A$ is mid point of $Q R$. $A \equiv \frac{(5 \hat{i}+3 \hat{j}+6 \hat{k})}{2}=\frac{5}{2} \hat{i}+\frac{3}{2} \hat{j}+3 \hat{k}$

In $\triangle P Q R,(4 \hat{i}+3 \hat{j}+6 \hat{k}),(2 \hat{i}+2 \hat{j}+3 \hat{k})$ and $(3…

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